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Chapter 6: Problem 10

A truck is moving northward at \(55 \mathrm{mi} / \mathrm{h}\). Later, it's moving eastward at the same speed. Has its kinetic energy changed? Has work been done on the truck? Has a force acted on the truck? Explain.

Short Answer

Expert verified
The truck's kinetic energy has not changed. However, work has been done on the truck, and a force has indeed acted on it to change the direction of its motion.

Step by step solution

01

Evaluate Change in Kinetic Energy

The truck's speed is the same in both cases (\(55 \mathrm{mi} / \mathrm{h}\)). Since kinetic energy (\(KE\)) is given by the formula \(KE = 1/2 m v^2\) where \(m\) is the mass of the object and \(v\) is its speed, the kinetic energy remains the same since neither the mass nor the speed changes.
02

Evaluate Work Done on the Truck

Work done (\(W\)) is the dot product of the force (\(F\)) and the displacement (\(d\)) vectors. Thus, \(W = \mathbf{F} . \mathbf{d}\). For work to be done, we need displacement in the direction of the force. Since the direction of truck's motion changes, this indicates a change in the velocity direction implying work to be done.
03

Determine if a force acted on the Truck

To change the direction of motion, the truck must have been subjected to a force. Newton's first law states that an object continues in a state of rest or of uniform motion unless compelled to change that state by a force impressed on it. Thus, to cause a change in direction of motion, a force must have acted on the truck.

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