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Chapter 6: Problem 8

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 kinetic energy of the truck hasn't changed because the speed remains the same. No work is done on the truck as there is no change in kinetic energy. However, a force must have acted on the truck to alter its direction.

Step by step solution

01

Analyze Kinetic Energy

Kinetic energy depends on the mass and velocity of a moving object, but it isn't dependent on the direction of movement. It is given by the formula \( KE = \frac{1}{2}mv^2 \), where \( m \) is the mass of the object and \( v \) is its velocity. In this case, when the truck moves northward or eastward at an equal speed, its magnitude of kinetic energy remains the same because the speed (and thus the velocity's magnitude) remains the same.
02

Identify Work Done

Work done on an object is associated with a change in kinetic energy. Since there is no change in the kinetic energy of the truck (same speed), no work is done on the truck while changing direction.
03

Determine if Force is Applied

Force on an object results in a change in motion of the object. A change in direction, as in the case of the truck moving northward to eastward, does mean a change in motion. Therefore, a force must have been applied to change the direction of the truck's motion.

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