A 12,000 N car starts from rest and rolls down a hill from a height of 10.0 m (s

Question

A 12,000 N car starts from rest and rolls down a hill from a height of 10.0 m (see figure). It then moves across a level surface and collides with a light spring-loaded guardrail. (a) Neglecting any losses due to friction, and ignoring the rotational kinetic energy of the wheels, find the maximum distance the spring is compressed. Assume a spring constant of 1.6 106 N/m. m (b) Calculate the maximum acceleration of the car after contact with the spring, assuming no frictional losses. m/s2 (c) If the spring is compressed by only 0.30 m, find the change in the mechanical energy due to friction. J

Explanation / Answer

a)

Using conservation of energy

mgh = 0.5*k*x^2

12000 * 10 = 0.5 * 1.6 *10^6 * x^2

x = 0.387 m

the maximum distance springs are compressed is 0.387 m

b)

mass of car = 12000/9.8 = 1224.5 Kg

Now, Using second law of motion

a = 12000 * 0.387/1224.5

a = 3.8 m/s^2

the maximum accleration is 3.8 m/s^2

c)

Loss due to friction = 0.5 * 1.6 *10^6 *(0.387^2 - -0.30^2)

Loss due to friction = 47815.2 J

the loss due to friction is 47815.2 J

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