Work-Kinetic Energy Balance - Example Problem 7.3-3

 

A 40-lb box has a velocity of 10 ft/s when it is at the top of the inclined surface shown, where θ = 40^o. The box is acted on by a constant force P = 5 lb that acts at the angle φ = 10^o with respect to the inclined surface. Determine the speed of the box after it slides d = 10 ft down the inclined surface. The coefficient of kinetic friction between the crate and the plane is μ_k = 0.4.

 

 

Given:

• W = 40 lb
• v₁ = 10 ft/s
• θ = 40^o
• φ = 10^o
• P = 5 lb
• d = 10 ft
• μ_k = 0.4

 

Find: v₂

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

When dealing with energy problems, it is important to identify energy states. Usually these states are the initial state and the final state, but there may be times where an intermediate state is required.

 

Click on the figure to see what was identified as state 1 and state 2.

 

This problem will be solved using the work-kinetic energy balance equation. Therefore, we need to determine which forces do work and which do not. The easiest way to determine this is to draw a free-body diagram.

 

Draw a fbd and click on the figure to see the results.

 

Which forces perform work?

 

P
N
W
F_fk