Answer to Question #283443 in Physics for Junard

Question

A 12N object is attached vertically by a string to a frictionless car that runs along a level track. The car with mass (m) kg covers a distance of 1.25m in 5s after it starts from rest. a)Find the final speed of the car. b)Find the loss in potential energy of 12 N object in falling through distance of 1.25m c) Gain in kinetic energy of the car and the hanging object. d)Mass of the car

Answer 1

a) Find the final speed of the car.

$$v=\dfrac{2d}t=0.5\text{ m/s}.$$

b) Find the loss in potential energy of 12 N object in falling through distance of 1.25 m.

$$\Delta E=mgh=12·1.25=15\text{ J}.$$

c) Gain in kinetic energy of the car and the hanging object.

$$\Delta KE=\dfrac12m_cv^2+\dfrac12 \dfrac Wg·2gh=(0.125m_c+15)\text{ J}.$$

d) Mass of the car:

$$m_c=m\dfrac{2d/t^2}{g-2d/t^2}=12.6\text{ g}$$