# How Far Will a Bundle Slide Up an Incline with Friction?

• h7u9i
In summary, the conversation involved finding the distance a 4.0 kg bundle will slide up a 30° incline with 128 J of kinetic energy and a coefficient of friction of 0.30. Through calculating the normal force and friction, it was determined that the bundle will slide 6.2 meters up the incline. However, there was initially confusion about the calculation of the normal force, which was later resolved by drawing a free body diagram and solving for the normal force using Fnet=ma.
h7u9i
A 4.0 kg bundle starts up a 30° incline with 128 J of kinetic energy. How far will it slide up the plane if the coefficient of friction is 0.30?So, I began finding the Normal
N=W(y)=4cos30=3.46

Then found friction

f=uN
f=.3*3.46=1.04

So
E=E
K=Ug + Q
K=mgh + fd
K=mg(dsin30)+fd
128=4(9.8)(.5)d+(1.04)d
128=20.64d
d=6.2m

But the answer says 4.3m. What's wrong?

Thanks!

EDIT:
So I figured it out... N=4*9.8cos30. Duh.

Last edited:
h7u9i said:
So I figured it out...
Glad things worked out. By the way, welcome to Physics Forums!

I had a similar problem (just the numbers changed). I get the whole h = dsin(30) thing, but why does Fn = mgcos(30)?

Ghostscythe said:
I had a similar problem (just the numbers changed). I get the whole h = dsin(30) thing, but why does Fn = mgcos(30)?
Draw a free body diagram. Take the direction of the normal force as the y-direction, apply Fnet=ma to the y-direction, and solve for Fn.

Sorry about that. So with the correct Normal force, the answer would be:

K=mg(dsin30)+fd
128=4(9.8)(.5)d+(1.04)d
128=19.6d+1.04d
128=20.64d
d=6.2m

So the answer should be 6.2m. Sorry for the mistake in the previous response. This calculation assumes that all the kinetic energy is converted into potential energy and work done against friction. Therefore, the bundle will slide up the incline for a distance of 6.2 meters before coming to a stop. The coefficient of friction of 0.30 will cause a significant amount of friction, resulting in the bundle only being able to travel a relatively short distance up the incline.

It's important to note that this calculation is based on ideal conditions and does not take into account any external factors such as air resistance or variations in the surface of the incline. In real-life situations, the distance the bundle would slide up the incline may vary. Additionally, the mass and initial velocity of the bundle also play a role in determining the distance it will slide.

Further studies and experiments can be conducted to better understand the movement of objects on an incline and the effects of friction. This information can also be used in practical applications such as designing efficient and safe transportation systems or improving the performance of machines and equipment that operate on inclines.

## 1. How does the angle of an incline affect the speed of an object?

The steeper the incline, the faster the object will move. This is because gravity has a greater pull on the object, causing it to accelerate down the incline at a faster rate.

## 2. What is the relationship between the weight of an object and its movement on an incline?

The weight of an object has a direct impact on its movement on an incline. Objects with a greater weight will experience a stronger pull from gravity, causing them to move faster down the incline.

## 3. How do friction and gravity play a role in movement on an incline?

Friction acts in the opposite direction of movement, slowing down the object's motion on an incline. Gravity, on the other hand, pulls the object down the incline. The balance between these two forces determines the speed and direction of the object's movement.

## 4. Does the material of the incline affect the movement of an object?

Yes, the material of the incline can affect the movement of an object. A rougher surface will create more friction, slowing down the object's motion. A smoother surface will have less friction, allowing for faster movement.

## 5. How does the length of an incline impact the distance an object will travel?

The longer the incline, the farther the object will travel. This is because the object has more time to accelerate and gain speed as it moves down the incline. However, other factors such as friction and the angle of the incline can also affect the distance traveled.

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