Question

A 3.5 kg model car travels down a ramp that is 2.3 m tall. At the top of the ramp, it is

moving with an initial speed of 3.4 m/s. At the bottom of the ramp is a 5,0 cm flat

surface that has a spring on the end of it, with a spring constant of 75.0 N/m.

What is the speed of the car just as it hits the spring? The ramp has a coefficieht

of friction of 0.12.

Answer 1

Apply conservation of energy:

$$\dfrac 12mv_i^2+mgh+\mu mgh/\sin\theta=\dfrac12mv_f^2,\\\space\\ v_f=\sqrt{v_i^2+2gh+2\mu gh/\sin\theta}.$$

To find the final velocity just before hitting the spring, you need to know the angle theta of the ramp above the incline.