Work-Kinetic Energy Balance - Example Problem 7.3-4

 

The motion of a pickup truck is arrested using a bed of loose sand AB and a set of crash barrels BC. If experiments show that the sand provides a rolling resistance of 120 lb per wheel and the crash barrels provide a resistance as shown in the graph, determine the distance x the 3120-lb truck penetrates the barrels if the truck's brakes fail and it is coasting at 70 mph when it approaches A. Take d = 70 ft and neglect the size of the truck.

 

 

Given:

• F_f = 4*120 lb (from A to B)
• F = 600x² lb (from B to C)
• d = 70 ft
• W = 3120 lb
• v_A = 70 mph = 102.7 ft/s

 

Find: x

 

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:

 

Note where the energy state A, B and C are located and then draw a free-body diagram of the truck.

 

 

 

 

Which two states should we apply the work-kinetic energy balance between to simplify our calculations?

 

A-B
B-C
A-C