A toy steam engine has a mass of 1.00 kg. The toy starts from rest and reaches a velocity of 4.00 m/s in a time of 3.00 seconds while covering a distance of 4.50 meters. During that time the toy takes in 30 J of heat. What is the change in the internal energy of the toy?

Question

Quizplus · Accepted Answer

Using the formula for work done on an object, work = force x distance, we can solve for the force applied to the toy:
work = force x distance
30 J = (1.00 kg)(4.00 m/s)^2 / 2 + force x 4.50 m
30 J = 8.00 J + force x 4.50 m
force = (30 J - 8.00 J) / 4.50 m
force = 4.67 N

Using the formula for internal energy, ΔU = Q - W, where Q is the heat transferred to the toy and W is the work done by the toy, we can solve for the change in internal energy:
ΔU = Q - W
ΔU = 30 J - (4.67 N x 4.50 m)
ΔU = 30 J - 21.02 J
ΔU = +8.98 J

Therefore, the change in the internal energy of the toy is +8.98 J, or answer choice D.

A Toy Steam Engine Has a Mass of 1