4. A 0.100-kg toy car is propelled by a compressed spring, as shown in the illustration below. The car follows a track that rises 0.180 m above the starting point. The spring is compressed 4.00 cm and has a force constant of 250.0 N/m. Assuming work done by friction to be negligible.
(a) Calculate how fast the car is going before it starts up the slope and
(b) Calculate how fast it is going at the top of the slope.
{The details of the path are unimportant because all forces are conservative-the car would have the same final speed if it took the alternate path shown.)
(c) Now, let's turn on friction on the path of the car. If the toy car was clocked at 0.500 m/s at the top the slope (i.e., slower speed than calculated in part (b)), find the work done on the toy car by friction.
{Hint: Find $W_{friction} = \Delta KE + \Delta PE_{gravitational} + \Delta PE_{spring}$}