# Distance Travelled Accounting for Friction

• merzperson
In summary, the box slides down a hill, starting from rest, and makes 8 trips across a rough surface before stopping.
merzperson

## Homework Statement

A 4.5 kg box slides down a 4.3-m-high frictionless hill, starting from rest, across a 2-m-long horizontal surface, then hits a horizontal spring with spring constant 460 N/m. The other end of the spring is frictionless, but the 2.0-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.25.

(a) What is the speed of the box just before reaching the rough surface?
(b) What is the speed of the box just before hitting the spring?
(c) How far is the spring compressed?
(d) Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?

Wf = -Ff*d

## The Attempt at a Solution

I got parts a-c easily, but now I'm stuck on part d.

What I did first was calculate the work done by friction on the box (Wf):

Wf = -Ff*d
Wf = -(11.03)(2) = -22.05J

Then I simply divided the initial energy (before the first crossing of the 2m section with friction) by the work done by friction to get the number of crossings before the box stops (loses all of its kinetic energy to heat):

Ei / Wf = C
190.44/22.05 = 8.64

This means that the box makes 8 complete trips across the frictional surface before stopping. MasteringPhysics says this is incorrect, where did I go wrong? Thanks!

merzperson said:

## Homework Statement

A 4.5 kg box slides down a 4.3-m-high frictionless hill, starting from rest, across a 2-m-long horizontal surface, then hits a horizontal spring with spring constant 460 N/m. The other end of the spring is frictionless, but the 2.0-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.25.

(d) Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?

[This means that the box makes 8 complete trips across the frictional surface before stopping. MasteringPhysics says this is incorrect, where did I go wrong? Thanks!

The assumption is that the energy robbed by friction is the same. Friction depends on the length of the path.

Thanks denverdoc for your reply!

However, I'm not sure what you're telling me. I did assume that the energy robbed by friction is the same every pass over the rough surface (when I calculated work done by friction). I also accounted for the length of the path when calculating the work of friction:
Wf = -Ff * d
Where d is displacement (rough path length).

Any other ideas? Thanks again!

EDIT:
I found out the distance of the rough section was 1.8m, so I did everything correctly just with a wrong number. Thanks everyone for your help!

Last edited:

## 1. What is "Distance Travelled Accounting for Friction"?

"Distance Travelled Accounting for Friction" is a scientific concept that takes into account the effects of friction on the distance an object travels. Friction is the force that opposes motion and can greatly affect the distance an object travels over a surface.

## 2. How does friction affect the distance an object travels?

Friction can cause a decrease in the distance an object travels because it acts in the opposite direction of motion. This means that the force of friction is working against the object's motion, slowing it down and causing it to travel a shorter distance.

## 3. Can friction ever increase the distance an object travels?

In some cases, friction can actually increase the distance an object travels. This is usually seen in instances where the object is rolling, such as a ball rolling down a hill. In this case, the friction between the ball and the surface can actually help propel the ball further, increasing its distance travelled.

## 4. How do scientists account for friction when calculating distance travelled?

To account for friction, scientists use mathematical equations and models that take into account the type of surface, the weight of the object, and other factors that can affect the amount of friction present. These calculations can then be used to determine the distance travelled by an object with a certain amount of friction present.

## 5. Why is it important to account for friction when measuring distance travelled?

Accounting for friction is important because it gives a more accurate representation of the distance an object has travelled. Ignoring friction can lead to incorrect measurements and predictions, which can have real-world consequences in fields such as engineering and physics.

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