Answers
Split up the forces into components acting parallel to and perpendicular to the slope. See the attached picture for the reference axes.
The box stays on the surface of the plane, so that the net force acting perpendicular to it is 0, and the only acceleration is applied in the parallel direction.
Let m be the mass of the box, θ the angle the plane makes with the ground, and a the acceleration of the box. By Newton's second law, we have
• net parallel force
∑ Force (//) = W (//) - F = m a
(that is, the net force in the parallel direction is the sum of the parallel component of the weight W and the friction F which acts in the negative direction)
• net perpendicular force
∑ Force (⟂) = W (⟂) + N = 0
Notice that
W (//) = W sin(θ) … … … which is positive since it points down the plane
W (⟂) = -W cos(θ) … … … which is negative since it points opposite the normal force N
So the equations become
W sin(θ) - F = m a
-W cos(θ) + N = 0
Solving for a gives
a = (W sin(θ) - F ) / m
which is good enough if you know the magnitude of the friction force.
If you don't, you can write F in terms of the coefficient of kinetic friction between the box and plane, µ, as
F = µ N
so that
a = (W sin(θ) - µ N ) / m
and the normal force itself has a magnitude of
N = W cos(θ)
so that
a = (W sin(θ) - µ W cos(θ) ) / m
The weight W has magnitude m g, where g is the magnitude of the acceleration due to gravity, so
a = (m g sin(θ) - µ m g cos(θ) ) / m
a = g (sin(θ) - µ cos(θ))
Related Questions
A sled is pulled with a force of 540 N at an angle of 40° with the horizontal. What are the horizontal and vertical components of this force?
Answers
Answer:
Fx = 467.65N
Fy = 270N
Explanation:
Given
Force = 540N
angle of inclination = 40 degree
Horizontal component Fx = Fcos 30
Fx = 540cos30
Fx = 540(0.8660)
Fx = 467.65N
Hence the horizontal component is 467.65N
Vertical component Fy = Fsin 30
Fy = 540sin30
Fy = 540(0.5)
Fy = 270N
Hence the vertical component is 270N
A certain heat engine does 30.2 kJ of work and dissipates 9.14 kJ of waste heat in a cyclical process.
A) What was the heat input to this engine?
B) What was its efficiency?
Answers
Answer:
a) [tex]H_{in}=39.34 kJ[/tex]
b) Efficiency=76.77%
Explanation:
a)
In order to solve this problem, we can use the following formula:
[tex]H_{in}=H_{out}+W[/tex]
the problem provides us with all the necessary information so we can directly use the formula:
[tex]H_{in}=9.14kJ+30.2kJ[/tex]
[tex]H_{in}=39.34 kJ[/tex]
b) In order to find the efficiency, we can use the following formula:
[tex]Efficiency=\frac{W}{H_{in}}*100\%[/tex]
so we get:
[tex]Efficiency=\frac{30.2kJ}{39.34kJ}*100\%[/tex]
Efficiency=76.77%
A projectile is fired horizontally from a height of 10 m above level ground. The projectile lands a horizontal distance of 15 m from where it was launched.
-Find the hang time for the projectile.
-Find the initial speed of a projectile.
-What are the x and y components of the projectile’s velocity the moment before it strikes the ground?
-At what speed will the projectile strike the ground?
Answers
Answer:
a)t = 1,43 s
b) V = 10,49 m/s
c) V₀ₓ = 10,49 m/s ; V₀y = 14,01 m/s
d) Vf = 17,5 m/s
Explanation:
According to the problem statement
V₀ = V₀ₓ and V₀y = 0
And at the end of the movement t = ? the distance y = 10 m
Therefore as
h = V₀y - (1/2)*g*t²
Vertical distance y = h = 10 = V₀y*t - 0,5 (-9,8)*t²
10 = 4,9*t²
t² = 10/4,9 ⇒ t² = 2,04 s
t = 1,43 s
a) 1,43 s is the time of movement
b) V₀ = V₀ₓ V₀y = 0 and V₀ₓ = Vₓ ( constant )
Just before touching the ground, the horizontal distance is
hd = 15 = Vₓ * t
Then 15 /1,43 = Vₓ = V₀ₓ
Vₓ = 10,49 m/s
Then initial speed is V = 10,49 m/s since V₀y = 0
Vf² = Vₓ² + Vy²
Vyf = V₀y - g*t
Vyf = 0 - 9,8 *1,43
Vyf = - 14,01 m/s
And finally the speed when the projectile strike the ground is:
Vf² = Vₓ² + Vy²
Vf = √ (10,49)² + (14,01)²
Vf = 17,50 m/s
An element or compound used to enhance a semiconductor is called a(n) ____.
Answers
Hope you guys have a good day! And, Merry Christmas!
Be/stay safe, and enjoy your break!
The element named boron can be used to enhance the properties of semiconductors.
What is a semiconductor?A semiconductor is a material that has electronic properties and has the value that falls in between a conductor. It can be a metallic copper or an insulator.
The rise in temperatures leads to a fall in resistivity. The element named boron can improve the electrical properties of the semiconductor as they form the impurities.
Find out more information about the element.
brainly.com/question/12389810
A statement of the second law of thermodynamics is that:__________.
a) spontaneous reactions are always exothermic.
b) energy is conserved in a chemical reaction that has a decrease in entropy.
c) spontaneous reactions are always endothermic.
d) in a spontaneous process, the entropy of the universe increases.
Answers
Answer:
in a spontaneous process, the entropy of the universe increases.
Explanation:
Entropy is a measure of of the degree of randomness or disorderliness in a system.
The second law of thermodynamics can be stated as follows; "in any spontaneous process, the entropy of the universe increases."
The universe here refers to the system's disorder and the disorder of the surroundings. Therefore, a spontaneous process can occur, in which the entropy of the system decreases, only if the entropy increases in the surroundings.
For instance, when ice freezes, the entropy of liquid water decreases, that is, the entropy of the system decreases. However, heat is given off to the surroundings and the entropy of the surroundings increases. This is an obvious expression of this law.
convert 100 Newton into dyne
Answers
Answer:10000000
Explanation:
Galaxy B moves away from galaxy A at 0.577 times the speed of light. Galaxy C moves away from galaxy B in the same direction at 0.731 times the speed of light. How fast does galaxy C recede from galaxy A?
Answers
Answer:
The value is [tex]p = 0.7556 c[/tex]
Explanation:
From the question we are told that
The speed at which galaxy B moves away from galaxy A is [tex]v = 0.577c[/tex]
Here c is the speed of light with value [tex]c = 3.0 *10^{8} \ m/s[/tex]
The speed at which galaxy C moves away from galaxy B is [tex]u = 0.731 c[/tex]
Generally from the equation of relative speed we have that
[tex]u = \frac{p - v}{ 1 - \frac{ p * v}{c^2} }[/tex]
Here p is the velocity at which galaxy C recede from galaxy A so
[tex]0.731c = \frac{p - 0.577c }{ 1 - \frac{ p * 0.577c}{c^2} }[/tex]
=> [tex]0.731c [1 - \frac{ p * 0.577}{c}] = p - 0.577c[/tex]
=> [tex]0.731c - 0.4218 p = p - 0.577c[/tex]
=> [tex]0.731c + 0.577c = p + 0.4218 p[/tex]
=> [tex]1.308 c = 1.731 p[/tex]
=> [tex]p = 0.7556 c[/tex]