# Mass on an inclined plane w/ FRICTION (use work energy theorem)

• bmx_Freestyle
In summary, we are trying to find the distance (s) that a 5kg mass will travel up an inclined plane with an initial velocity of 40m/s at a 30° angle, given a coefficient of friction of 0.15. Using the work energy theorem, we can set up equations to solve for s and the final velocity (vf) when the mass returns to the bottom of the ramp. To find the percentage of lost mechanical energy, we need to consider the work done by friction and the work done by gravity. By setting up and solving equations, we can find that the mass will travel 0.598m up the ramp and have a final velocity of 2.23m/s. The percentage of

#### bmx_Freestyle

Mass on an inclined plane with friction!
There is a mass at the bottom of an inclined plane. It travels with an initial velocity up the inclined plane at an angle θ. There is a coefficient of friction on the ramp. How far up the ramp will the mass go before stopping? What is the speed of the block when it returns to the bottom of the ramp? What percent of the initial total mechanical energy was lost during the mass's trip (going up and then back down?
m=5 kg
vo=40 m/s
θ=30°
S=the distance you are looking for
Coefficient of friction (μ) = 0.15

Work energy theorem=mg(hf-ho) + 1/2 m (vf^2-vo^2) +fs

Attempt:
i set up the work energy theorem and simplified it down to "work=mghf-1/2mvo^s+μ
mgs" and solved for s
and then i used "work= -mgho + 1/2mvf^s +μ
mgs to solve for vf
i honestly had no clue what to do for the third part of this problem

I don't think my answers are right bc i got 0.598 m fr the first part and 2.23 m/s fr the second part...and i couldn't figure out the third part

Help would be appreciated. Thank u very much to all!

Last edited:
work= -mgho + 1/2mvf^s +μ
I think this should be 0 = mg*h - ½m⋅Vo² + μ*Fn*s
since no work is done except the included friction work; it has initial velocity but the final velocity is zero, h is the height it goes up. Express h in terms of s and the angle of the ramp. You will solve for s to find the answer. The normal force, Fn needs to be figured out from the force of gravity and the angle.

## 1. What is the work-energy theorem?

The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy. In other words, the work done by all the forces acting on an object results in the object gaining or losing kinetic energy.

## 2. How does friction affect the motion of an object on an inclined plane?

Friction is a force that opposes motion and acts in the opposite direction of the object's velocity. On an inclined plane, friction acts in the direction opposite to the object's motion, causing it to slow down and eventually come to a stop.

## 3. How do you calculate the work done by friction on an inclined plane?

The work done by friction on an inclined plane can be calculated using the formula W = Fdcosθ, where W is the work done, F is the force of friction, d is the distance traveled, and θ is the angle between the force of friction and the displacement of the object.

## 4. What is the relationship between the work done by friction and the change in kinetic energy of an object on an inclined plane?

According to the work-energy theorem, the work done by friction is equal to the change in kinetic energy of the object. This means that as the object moves down the inclined plane, the work done by friction will result in a decrease in the object's kinetic energy.

## 5. How does the presence of friction affect the efficiency of an inclined plane?

Friction always causes a loss of energy, so the presence of friction on an inclined plane will decrease its efficiency. This means that more work is required to move an object up an inclined plane with friction compared to one without friction.