# The Work Done on a Sliding Box: How to Calculate Friction and Applied Force

• murrskeez
In summary, the conversation is about finding the magnitude of the average frictional force acting on a box that is sliding along a horizontal surface, and determining the work done on the box by a person after the box comes to rest at a position x1 and is pushed to a speed v1 until it reaches a position x2. The correct answer for part A is Ff=(mv0^2)/(2x1), and for part B, the work done is -(mv0^2(x2-x1))/(2x1) + (mv1^2)/2. However, this answer also needs to include v1, so setting the work done equal to the change in kinetic energy between x1 and x2, the final
murrskeez

## Homework Statement

A box of mass m is sliding along a horizontal surface.
Part A) The box leaves position x=0 with a speed v0. The box is slowed by a constant frictional force until it comes to rest at a position x=x1. Find Ff, the magnitude of the average frictional force that acts on the box. (express in terms of m, v0, and x1.
I found the correct answer to part A...(Ff=(mv02)/2x1)

Part B) After the box comes to rest at a position x1, a person starts pushing the box giving it a speed v1. When the box reaches position x2 (where x2>x1), how much work Wp has the person done on the box? Assume that the box reaches x2 after a person has accelerated it from rest to speed v1. Express the work in terms of m,v0,x1,x2, and v1.

W=ΔKE
W=F*d

## The Attempt at a Solution

So I figured that the total work would be the work done in part A (-(mv02)/2x1)*(x1)
added to the work done between x1 and x2:
-(mv02(x2-x1))/2x1

however when I add these two solutions, it tells me that the answer needs to include v1. So then I thought to solve for v1 by setting the work done between x1 and x2 equal to the change in kinetic energy between that time frame which gave me:

KE = (mv12)/2 = work between x1 and x2

v02=(x1v12)/-(x2-x1)

so that allowed me to have v1 in my final answer...but mastering physics is still telling me it's incorrect.

You were nearly right the first time - what distance does the friction force act over?

1 person

## 1. What is "Work on a Sliding Box"?

"Work on a Sliding Box" is a scientific concept that refers to the amount of energy required to move a box across a surface while maintaining a constant speed.

## 2. How is "Work on a Sliding Box" calculated?

"Work on a Sliding Box" can be calculated by multiplying the force applied to the box by the distance it travels. This formula is represented as W = Fd, where W is work, F is force, and d is distance.

## 3. What factors affect the amount of work required on a sliding box?

The amount of work required on a sliding box is affected by the force applied, the distance traveled, and the coefficient of friction between the box and the surface it is sliding on. Other factors such as the weight of the box and the surface type may also have an impact.

## 4. How does the angle of the surface affect the work on a sliding box?

The angle of the surface can have a significant impact on the work required on a sliding box. In general, the steeper the angle of the surface, the more work will be required to move the box. This is because the force needed to overcome gravity and maintain a constant speed increases as the angle increases.

## 5. What are some real-life applications of "Work on a Sliding Box"?

"Work on a Sliding Box" has various applications in everyday life, such as pushing a book across a table, pushing a shopping cart, or pulling a suitcase with wheels. It also has important implications in the fields of engineering, physics, and transportation, as it helps determine the amount of energy needed to move objects across different surfaces.

• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
975
• Introductory Physics Homework Help
Replies
2
Views
207
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
1K
• Introductory Physics Homework Help
Replies
25
Views
2K
• Introductory Physics Homework Help
Replies
29
Views
1K
• Introductory Physics Homework Help
Replies
8
Views
900
• Introductory Physics Homework Help
Replies
58
Views
3K