The equation that can be used to calculate the mechanical advantage of a simple machine is as follows: MA = delta x0 / delta x1 (option D).
How to calculate mechanical advantage?Mechanical advantage is the ratio of the output force produced by a machine (especially a simple machine) to the applied input force.
The mechanical advantage (MA) is used to analyze the forces in simple machines like levers and pulleys.
Mechanical advantage = Fo/Fi
Where;
Fo = output forceFi = input forceAccording to this question, option D best describes the equation that can be used to calculate the mechanical advantage of a simple machine.
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what is the acceleration of the dog sled??
Answer:
a=2m/s^2
Explanation:
F=ma => a=F/m=100/50=2m/s^2
darcel runs the simulation for the large version of each object. what can he say in general about the energies of the objects in the simulation as they roll down the incline? (select all that apply.)
The total energy of the system remains constant and is equal to the gravitational potential energy of the object at the top of the incline.
What is gravitational potential energy?Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. This energy is determined by the objects mass, height and the strength of the gravitational field. Gravitational potential energy increases as the object moves higher from the ground and its mass increases. Gravitational potential energy can be converted into kinetic energy when an object falls or moves down a slope.
The total kinetic energy of a rolling object is the sum of the rotational kinetic energy about the center of mass and the translational kinetic energy of the center of mass.
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Complete Question:
Darcel runs the simulation for the large version of each object. What can he say in general about the energies of the objects in the simulation as they roll down the incline? (Select all that apply.)
"The total energy of the system remains constant and is equal to the gravitational potential energy of the object at the top of the incline.""The total kinetic energy of a rolling object is the sum of the rotational kinetic energy about the center of mass and the translational kinetic energy of the center of mass.""The translational kinetic energy is always greater than the rotational kinetic energy.""The potential energy of the system remains constant, and is equal to the total energy."
A 3.0-cm object is placed 8.0 cm in front of a mirror. The virtual image is 4.0 cm further from the mirror when the mirror is concave than when it is planar.
. Determine the focal length of the concave mirror. (a) 6.0 cm (c) 24 cm (e) 96 cm (b) 12 cm (d) 48 cm
. Determine the image height in the concave mirror. (a) 0.5 (c) 2.0 (e) 4.5 (b) 1.5 (d) 3.0
The focal length and image height of the concave mirror is 24cm and 4.5cm respectively. So, the correct options are (C) and (E) respectively.
What is Concave mirror?A concave mirror is defined as a reflective surface that is curved inward and away from the light source to reflect light inward at a focal point. Convex mirror is the image formed by a concave mirror shows different types of image depending on the distance between the object and the mirror.
The focal length of the mirror is :
[tex]1/f = 1/d_o + 1/d_i[/tex]
where, [tex]d_o[/tex] and [tex]d_i[/tex] are distances of object and image respectively
For normal mirror[tex]d_o = d_i = 8[/tex]
For concave mirror [tex]d_o = 8; d_i = 12[/tex]
1/f = 1/8 - 1/12 (following sign conventions)
f = 24cm
object height = 3cm
Height of the image is 3*12/8 = 4.5cm
Thus, the focal length and image height of the concave mirror is 24cm and 4.5cm respectively. So, the correct options are (C) and (E) respectively.
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a baseball bat collides with a 0.145 kg baseball moving with an initial velocity of 35 m/s to the left. if the collision lasts 0.005 seconds and the final velocity of the ball is 25 m/s to the right, what was the force of the bat on the ball?
According to Newton's third law of motion, the ball imparts an equal and opposite force on the bat. i.e 290 N
Given that,
The mass of the ball = .145 kg
initial velocity of 35 m/s
collision lasts 0.005 seconds
final velocity of the ball is 25 m/s
We have momentum = mass x velocity.
a) Initial momentum = 0.145*35 = 5.075 kg-m/s
b) Final momentum = 0.145*25 = 3.625 kg-m/s
c) Change in momentum = 5.075 - 3.625 = 1.45 kg-m/s
Impulse = Force x time = change in momentum
F = change in momentum/time = 1.45/0.005 = 290 N
d) By Newton's third law of motion, the ball imparts an
equal and opposite force on the bat.
therefore, Force = 290 N.
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which types of geometrical symmetry does a sphere have?
A. Rotational symmetry
B. Reflection symmetry
C. Translational symmetry
The sphere has two geometrical symmetries, they are
1. Rotational symmetry
2. Reflection symmetry
What is Rotational Symmetry?Rotational symmetry: An object's ability to maintain the same shape when rotated about its own axis is known as rotational symmetry. When turned 180 degrees or at certain angles, either clockwise or counterclockwise, many geometrical forms appear to be symmetrical. Examples include the square, circle, hexagon, and more.
What is Reflection Symmetry?Reflection symmetry: Symmetry with regard to reflections is known as reflection symmetry. Mirror or line symmetry are other names for reflection symmetry. If a figure is divided into two halves, one of the halves must be the mirror image of the other, according to this rule.
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Geometrical symmetry states that a sphere has reflection symmetry. The orthogonal group O is the name of the symmetry group of the sphere, which includes reflections (3).
Which symmetry in geometry does a spherical possess? Geometrical symmetry states that a sphere has reflection symmetry. The orthogonal group O is the name of the symmetry group of the sphere, which includes reflections (3). The special orthogonal group SO is the symmetry group that only has rotations (3).Further investigation reveals that two electrons spinning in the same direction at the same time cannot be positioned in the same location due to the two-fold rotational property of spherical symmetry.Spherical geometry is the three-dimensional, spherical counterpart of Euclidean or planar geometry and is described as "the study of figures on the surface of a sphere" (MathWorld).In physics, a body is considered to have spherical symmetry if only its density varies with distance from the center.To learn more about geometrical symmetry refer
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students analyze their data from a gravity experiment. they find that objects fall at a greater speed from a greater height than from a lower height. what can they conclude?(1 point)
An experiment using gravity lead students to the conclusion that gravity affects the speed of objects.
This is thanks to the experiment that they conducted, which showed that objects fall faster when released from a higher height than when released from a lower height. This indicates that gravity is accelerating the objects as they fall.
The rate of acceleration is proportional to the force of gravity, meaning that the more gravity that is present, the faster the objects will fall. This means that the higher the height, the greater the force of gravity and the faster the objects will fall.
Students can also conclude that the time taken for an object to fall is greater from a lower height than one from a higher height. This is because the higher the height, the greater the force of gravity, meaning that the objects reach their terminal velocity quicker. Terminal velocity is the maximum speed an object will reach, and this can be reached quicker from higher heights.
Overall, students can conclude that gravity affects the speed of objects as they fall and that the higher the height, the faster the objects will fall. This is due to the force of gravity increasing with height, meaning that the objects reach their terminal velocity quicker, leading to faster falls.
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Answer:
1. Mass is the measure of the amount of matter in an object.
2. The objects do not have the same size, shape, or mass, so any differences in drop times cannot be attributed to one variable.
3. Gravity is a force that attracts objects with mass toward each other.
4. by repeating the experiment several times
5. The longer an object falls, the more gravity increases its speed.
how many coulombs of positive charge are there in 1.54 kg of plutonium, given that its atomic mass is 244 and each plutonium atom has 94 protons?
Given that plutonium has an atomic mass of 244 and 94 protons per atom, there are 1.48108 C coulombs with positive charge present in 1.54 per kg plutonium.
What do the protons in atoms do?The particle possesses an electrical charge that is positive and opposite to the electron's. A single protons would weigh only 1.673? 10-27 kilograms if it were isolated, which is just a little bit less than a neutron.
What is the name for protons?Although protons were once thought of as elementary particles, the Standard Model of subatomic particles now recognizes them as composite particles made up of three valence quark, and they are grouped alongside neutrons as hadrons.
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if the electric field at a distance r away from charge q is 36 n/c, what is the ratio of the electric fields at r, 2r, and 3r?
The ratio of electric fields at r, 2r, and 3r at a distance r away from the charge q is 36 n/c is calculated to be 36:9:4.
Every point in space where a charge, in whatever form, is present can be thought of as having an electric field surrounding it. An alternative name for an electric field is the electric force per unit charge.
The relation between electric field intensity, charge and distance is known to be E = k Q/r².
where, E is the electric field
r is the distance
It is clear that E ∝ 1/r²
If the distance is 1/2r, E = 1/(2r)² = 1/4r² = E/4
If the distance is 1/3r, E = 1/(3r)² = 1/9r² = E/9
In this problem, E is given as 36 n/c, so the ratio is 36/4 = 9 and 36/9 = 4
Hence, the required ratio is 36:9:4.
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Light travels up through a pond of water of critical angle 49°. What happens at the surface if the angle of incidence is 30°?
The light will refract and pass through the water's surface at an angle of incidence greater than the critical angle if the angle of incidence is 30 degrees, leading to total internal reflection.
How does a substance's refractive index impact the angle of refraction?
A substance's refractive index is a measurement of how much light is bent as it passes through it. The angle of refraction increases with increasing refractive index. The angle of refraction increases as light travels from a medium with a lower refractive index, like air, to a medium with a higher refractive index, like water or glass. Because of this, as light enters the higher refractive zone, it bends more sharply. .
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David wrote Five $10 Checks and two check for 100 each
What is the net work done on a 0.430kg football as, starting from rest, it is thrown at
12.7m/s?
a. Wnet = 0
b. Wnet = 34.7J
c. Wnet = 69.4J
d. Wnet = 2.73J
The work that is done by the ball is 2.73J.
What is the net force?We have to note that the net force has to do with the force that we can obtain from the Newton's law. We have to note that from the use of the Newton's law that we are going to have that;
F = ma
F = force
m = mass
a = acceleration
Assuming the time to be 1s
a = 12.7 - 0/1
a = 12.7m/s^2
Then the work that is done is obtained by the use of the formula stated above as follows;
F = 0.430kg * 12.7m/s^2
F = 2.73J
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If all 152 million discarded phones in America were recycled, how many pounds of each mineral would be recovered?
Gold- _____pounds
Silver- ____ pounds
palladium- ______ pounds
Copper- _____ pounds
7,600
3,040,000
3,040
83,600
Please help asap!! Thank youuuuuu!
Gold 7,600 pounds, Silver 83,600 pounds, palladium 3,040 pounds and
Copper 3,040,000 pounds.
What is meant by pounds?
The name of a unit of currency is pound. Both presently and in the past, it was employed in many different nations.The Roman era on the continent of Europe is where the British pound first appeared. From the Latin word "poundus," which means "weight," comes its name. The elaborate L in Libra is where the £ sign originated. The pound, which represented one pound of silver weight, was a monetary unit in Anglo-Saxon England as early as 775 AD.The two units are equal because one lb is another term for one pound. 1 pound equals 1 lb. Actually, "lb" is an acronym for "pound."To learn more about pounds refer to
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The initial and final velocities of a particle are shown in the figure below. Find the particle's average acceleration if the change in velocity takes place in a 11.5 s interval. (Let vi = 29.0 m/s and vf = 18.0 m/s.)
Answer:
To calculate the average acceleration of the particle, we use the formula a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time interval. In this case, a = (18.0 m/s - 29.0 m/s)/11.5 s = -2.3 m/s2. Therefore, the average acceleration of the particle is -2.3 m/s2.
If the charging collar has a positive charge, what will be the net charge on a droplet separating from the stream?
(a)Positive
(b)Negative
(c)Neutral
(d)The charge will depend on the type of cell
The net charge on a droplet separating from the stream will be (b) Negative.
How does the charge on a droplet affect its interaction with other charged objects?The charge on a droplet affects its interaction with other charged objects based on the principle of electrostatics, which states that like charges repel each other and opposite charges attract each other. A droplet that carries a positive charge will experience a repulsion force when it comes into contact with another positively charged object. On the other hand, a droplet that carries a negative charge will experience an attraction force when it comes into contact with a positively charged object. The strength of this interaction is dependent on the magnitude of the charges and the distance between the droplet and the other charged object.
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what is the possible cause of an engine running rich at full throttle if it is equipped with a float type carburetor
Clogged main air bleed is the possible cause of an engine running rich at full throttle if it is equipped with a float type carburetor .
Bleed air is mostly used in civil aircraft to feed the environmental control system with air, which maintains pressure in the cabin. Bleed air is also utilised to prevent ice from forming on important sections of the aircraft, including the wing leading edges. the throttle valve of a carburetor with a float design.
This improves fuel vaporisation and discharge management, especially at low engine speeds. In the carburetor barrel, close to one end of the venturi, is where the throttle, or butterfly valve, is situated. By adjusting the airflow to the engine, it offers a way to control engine speed or power production. The float needle valve is worn or otherwise not seated if a float-type carburetor spills fuel while the engine is turned off.
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If an engine has a float type carburetor, a clogged main air bleed could be the reason why it runs rich when the throttle is fully opened.
Bleed air is mostly utilized in civil airplanes to supply air to the environmental control system, which maintains cabin pressure. Bleed air is also used to stop ice from accumulating on critical areas of the aircraft, such as the wing leading edges. a carburetor's throttle valve with a float arrangement.
This facilitates better fuel vaporization and discharge control, particularly at low engine speeds. The butterfly valve, also known as the throttle, is located inside the carburetor barrel, close to one end of the venturi. It provides a technique to regulate engine speed or power output by changing the airflow to the engine. If a float-type carburetor leaks fuel when the engine is off, the float needle valve is worn or otherwise not seated.
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question a particle with a small electric charge is moved in an electric field by an external force. when the particle is moved along an electric potential isoline, in what direction, if any, is the force exerted by the electric field on the particle?
A particle with a small electric charge is moved in an electric field by an external force. When the particle is moved along an electric potential isoline, in what direction, if any, The force exerted by Perpendicular to the direction of the particle's motion.
What Is Electric Charge“Electric Charge is the property of subatomic particles that causes it to experience a force when placed in an electric and magnetic field.”
Electric charges are of two types: Positive and Negative, commonly carried by charge carriers protons and electrons.
Examples of the types of charges are subatomic particles or the particles of matter:
Protons are positively charged.Electrons are negatively charged.Neutrons have zero charge.Is Electric Charge a Vector QuantityElectric charge is a scalar quantity. Apart from having a magnitude and direction, a quantity to be termed a vector should also obey the laws of vector addition, such as triangle law of vector addition and parallelogram law of vector addition; only then the quantity is said to be a vector quantity. When two currents meet at a junction, in the case of an electric current, the resultant current of these will be an algebraic sum and not the vector sum. Therefore, an electric current is a scalar quantity, although it possesses magnitude and direction.
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A force is required to keep a 5kg mass moving round a cycle of 3.5m at a speed of 7ms^-1. What is the speed of the force if tripled
The speed of the of the object if the force is tripled is 12.12 m/s.
What is the centripetal force?The centripetal force acting on an object moving in a circular path is calculated by applying the following formula as shown below.
F = mv² / r
where;
m is the mass of the objectv is the speedr is the radiusF = ( 5 x 7² ) / 3.5
F = 70 N
When the force is tripled, the new force becomes;
F' = 3 x 70 N
F' = 210 N
The new speed of the object is calculated as follows;
F = mv² / r
v² = Fr / m
v = √ ( Fr / m )
v = √ ( 210 x 3.5 / 5 )
v = 12.12 m/s
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the dwarf planet pluto has 1/500 the mass and 1/15 the radius of earth. what is the value of g (in m/s2) on the surface of pluto? use g
The value of g (gravity on the surface of Pluto is roughly [tex]0.632 m/s^2[/tex]
To find the value of g (speed increase because of gravity) on the surface of Pluto, we can utilize the condition:
[tex]g = GM/R^2,[/tex]
where G is the gravitational steady[tex](6.67 x 10^-11 m^3/kg s^2)[/tex], M is the mass of Pluto, and R is the radius of Pluto.
Since we realize that the mass of Pluto is 1/500 the mass of Earth and the radius of Pluto is 1/15 the range of Earth, we can utilize these qualities to work out g on Pluto.
To begin with, we'll find the mass of Pluto in kg by multiplying the mass of Earth [tex](5.972 x 10^{24} kg)[/tex] by 1/500:
[tex]M = 5.972 x 10^{24} kg * (1/500)[/tex] = [tex]1.1944 x 10^{22} kg[/tex][tex]1.1944 x 10^{22} kg[/tex]
Then, we'll find the radius of Pluto in meters by multiplying the radius of Earth (6,371 km) by 1/15:
R = 6,371 km * (1/15) = 424.73 km = 424,730 m
At long last, we can utilize these qualities to work out g on Pluto:
g = [tex](6.67 x 10^-11 m^3/kg s^2)[/tex] [tex]* (1.1944 x 10^{22} kg)/(424,730 m)^2[/tex]
[tex]g =[/tex] [tex]0.632 m/s^2[/tex]
So the acceleration due to gravity on the surface of Pluto is rough [tex]0.632 m/s^2[/tex], which is around 6.5% of the speed increase because of gravity on the earth.
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in the absence of air resistance, what launch angle of a projectile results in the longest range?
In the absence of air resistance, the launch angle of the projectile results in the longest range is found to be 45°.
What is the launch angle?The launch angle may be defined as the vertical angle at which the ball leaves a player's bat after being struck. Average Launch Angle (aLA) is calculated by dividing the sum of all Launch Angles by all Batted Ball Events.
The angle between an input ray and the fiber axis. If the end face of the fiber is perpendicular to the fiber axis, the launch angle is equal to the angle of incidence. The angle of a projectile's initial velocity is definitely calculated when measured from the horizontal direction. These angles are typically 90° or less.
Therefore, in the absence of air resistance, the launch angle of the projectile results in the longest range is found to be 45°.
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define speed in your own words. why does a car speedometer only have positive values, even though you can move in reverse?
Speed is defined as the rate of change of distance over time. It has the dimension of distance x time. The SI unit of speed is a combination of the base unit of distance and the base unit of time. The SI unit for speed is meters per second.
Speed is the speed at which an object's position changes, measured in meters per second. For example, if an object starts at the origin and moves 3 meters in 3 seconds, its speed is 1 meter/second. A car's speedometer only has positive numbers, but it can run backwards. This is because it measures speed based on the distance the car travels, not the direction the car is heading.
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an empty truck with a mass of 2500 kg has an engine that will accelerate at a rate of 1.5 m/s what will happen if the truck is carrying an additional weight of 1500kg
The acceleration of the truck when an additional weight of 1500kg is added to an empty truck of mass 2500kg is 0.9375 m/s².
What is Acceleration?Acceleration is the rate of change of the velocity of an object with respect to the time interval. Acceleration is a vector quantity. The orientation of an object's acceleration is given through the orientation of the net force which is acting up on that object.
Force = Mass × acceleration
Empty truck Mass = 2500 kg
Acceleration = 1.5 m/s²
Force = 2500 × 1.5
Force = 3750 N
Additional load of 1500 kg
Total Mass = (2500 + 1500)kg = 4000 kg
3750 = 4000 × a
a = 3750 /4000
a = 0.9375 m/s²
Acceleration when the truck has an additional load of 1500 kg is 0.9375 m/s².
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four identical charges q are placed at the corners of a square of side a. find the magnitude of the electric field at one charge produced by the other three charges
The magnitude formula is able to test the stability of the induced current F put on a charge [q 1] as an effect of another charge [q 2: [F = frac(k,q,r)] The Coulomb's ratio (k) or the distance (r) between two are present here.
How do you define magnitude?huge or highly significant: An average man would have given up due of the task's size. earth science The brilliance of a galaxy as seen from Earth is also measured by magnitude.
Does size equal worth?A quantity's measuring or absolute value is referred to as its magnitude. A positive actual number serves as the symbol for a magnitude. A magnitude can be defined as a quantity's size in simple terms.
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What is the speed of a car that goes 150 km in 45 minutes. What is its velocity is it is traveling south?
The speed of the car is 200 km/hour.
The velocity of the car is 200 km/hour in south direction.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
Distance travelled is = 150 km.
Time taken is = 45 minute = 0.75 hour.
Hence, the speed of the car is = 150/0.75 km/hour = 200 km/hour.
As the car is traveling south, the velocity of the car is 200 km/hour in south direction.
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by which element are gamma rays produced
Answer: Some elements like potassium, uranium, and thorium are naturally radioactive and give off gamma rays as they decay, but all elements can be excited by collisions with cosmic rays to produce gamma rays. The HEND and Neutron Spectrometers on GRS directly detect scattered neutrons, and the Gamma Sensor detects the gamma rays.
Explanation: searching
A sample of an ideal gas expands to twice its initial volume. In which type of expansion does the gas perform the least work?
A) A free expansion, in which the gas expands suddenly into a vacuum
B) A slow, gradual expansion in which heat is added to the gas
C) A rapid isothermal compression of the gas to half its initial volume, followed by a slow expansion in which heat is added
A free expansion, in which the gas expands suddenly into a vacuum, is the type of expansion in which the gas performs the least work. So correct option is A).
What do you mean by ideal gas?An ideal gas is a theoretical gas that is considered to have several idealized characteristics. These include:
No intermolecular forces: The particles in an ideal gas are considered to occupy a large volume relative to the size of the individual particles, and they are not considered to interact with one another through intermolecular forces.Completely random motion: The particles in an ideal gas are considered to move randomly in any direction, with no preferential direction of motion.Point-like particles: The particles in an ideal gas are considered to be point-like, with no size or structure.Constant volume: The volume of an ideal gas is considered to be constant and does not change with pressure or temperature.These idealized conditions are used to make predictions about the behavior of real gases in various physical systems, and the concept of an ideal gas is a useful tool for understanding and modeling the behavior of gases.
During a free expansion, no external forces are acting on the gas, and no work is done by or on the gas. This is because work is defined as the transfer of energy from one system to another, and in a free expansion, the gas is isolated from its surroundings, so no energy transfer takes place. In contrast, during a slow, gradual expansion in which heat is added to the gas, or a rapid isothermal compression of the gas followed by a slow expansion in which heat is added, external forces are acting on the gas, and work is done on the gas. In these cases, the gas performs more work because energy is transferred from the surroundings to the gas.
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A group of people are pushing a stalled car with a mass of 1100 kg. If they push with a net force of 350 Newtons for 10 seconds, what is the car’s velocity?
The car would move with a velocity of 3.182 m/s if they applied a net force of 350 Newtons for 10 seconds.
What is meant by net force?The net force is the total of all the forces operating on an object, according to its definition. Mass can be accelerated by net force. Whether a body is at rest or in motion, another force is at work on it. When a system has a lot of forces acting on it, the phrase "net force" is employed.
The net force, sometimes referred to as the resultant force, is the total force acting concurrently on an item. For instance, a rope being pulled from the right by a force of five newtons and from the left by a force of three newtons will experience a net force of two newtons from the right.
A bunch of individuals are pulling an automobile that weighs 1100 kg and is stuck in traffic. The car would move with a velocity of 3.182 m/s if they applied a net force of 350 Newtons for 10 seconds.
Therefore, the car’s velocity would be 3.182 m/s.
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A hot air balloon is moving vertically upwards with a constant speed of 3.00 m/s. A sandbag is dropped from the balloon. It takes 5.00 seconds for the sandbag to fall to the ground. What was the height of the balloon when the sandbag was released?
The height of the balloon when the sandbag was released is 108m which is moving vertically upwards with a constant speed of 3.00 m/s.
Given the constant speed of hot air balloon (v) = 3m/s
Time taken by the sandbag to fall to the ground (t) = 5s
As the balloon is moving upwards and sandbag is falling downwards they both are in motion opposite to each other.
Let the initial speed of sandbag (u) = 3m/s
Acceleration due to gravity (a) = -9.8m/s^2
From equation of motion we have: s = ut + 1/2at^2
s = 3 x 5 + 1/2(-9.8)(5)^2
s = -108m
Hence the height of the balloon when the sandbag was released is 108m.
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Rank the colored waves in order of highest frequency to lowest frequency. highest frequency lowest frequency
Answer:
Explanation:
Highest → Lowest frequency
Violet→Indigo→Blue→Green→Yellow→Orange→Red
susan replaces all the old incandescent bulbs in her home with led bulbs. by the time she was done, she had replaced 45 lightbulbs with more energy-efficient varieties. how much should she expect to save in energy bills each year?
Susan should expect to save approximately $3,822.5 in energy bills each year by replacing her incandescent bulbs with LED bulbs.
LED bulbs are much more energy-efficient than incandescent bulbs. They use significantly less power and last much longer.
One of the ways to estimate energy savings is to calculate the difference in power consumption between an incandescent bulb and a LED bulb of the same brightness.
For example, if an incandescent bulb uses 60 watts and a LED bulb uses 10 watts to produce the same amount of light, the LED bulb will use 83% less energy than the incandescent bulb.
If we assume that each LED bulb last for an average of 25,000 hours and the incandescent last for an average of 1,200 hours and the cost of electricity is $0.13 per kWh, the savings will be:
(45 bulbs * (60-10)W/1000) * 25000hrs/yr * $0.13/kWh = $3,822.5
So, Susan should expect to save approximately $3,822.5 in energy bills each year by replacing her incandescent bulbs with LED bulbs.
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Three oak blocks, ma = 4.0 kg, mB = 6.0 kg, and mc = 3.0 kg, are positioned next to each
other on a dry, horizontal oak surface. Use the data from Table 5.1 on page 148 to answer
these questions.
(a) What horizontal force must be applied to accelerate the blocks at 1.4 m/s² [forward]. (Assume that the blocks are already moving at a constant velocity.)
(b) Calculate the force exerted by ma on mc.
(c) Calculate the force exerted by me on mA.
Friction Force Calculation.
(a) The horizontal force required to accelerate the blocks at 1.4 m/s² is the combined force of friction acting on the three blocks. To find this force, we need to know the coefficient of friction between the blocks and the surface.
According to Table 5.1, the coefficient of friction for oak on oak is 0.4. To find the force of friction, we use the equation: friction force = coefficient of friction * normal force.
The normal force is the force acting perpendicular to the surface and is equal to the combined weight of the three blocks, which is
ma + mb + mc = 4.0 kg + 6.0 kg + 3.0 kg = 13.0 kg. The force of friction is then: friction force = 0.4 * 13.0 kg * 9.8 m/s² = 52.24 N.
(b) To find the force exerted by ma on mc, we need to find the force of friction acting on ma and mc. The force of friction on ma is: friction force = coefficient of friction * normal force = 0.4 * 4.0 kg * 9.8 m/s² = 15.68 N.
The force of friction on mc is: friction force = coefficient of friction * normal force = 0.4 * 3.0 kg * 9.8 m/s² = 11.76 N.
The force exerted by ma on mc is the force of friction on ma + the force of friction on mc = 15.68 N + 11.76 N = 27.44 N
(c) To find the force exerted by mc on ma, we can use the same method as above. The force of friction on mc is: friction force = coefficient of friction * normal force = 0.4 * 3.0 kg * 9.8 m/s² = 11.76 N.
The force of friction on ma is: friction force = coefficient of friction * normal force = 0.4 * 4.0 kg * 9.8 m/s² = 15.68 N.
The force exerted by mc on ma is the force of friction on mc + the force of friction on ma = 11.76 N + 15.68 N = 27.44 N
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