Use the worked example above to help you solve this problem. A 14,000 N car star

Question

Use the worked example above to help you solve this problem. A 14,000 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 times 10^6 N/m..42 m (b) Calculate the maximum acceleration of the car after contact with the spring, assuming no frictional losses. 50 Your response differs from the correct answer by more than 10%. Double check your calculations. m/s^2 (c) If the spring is compressed by only 0.30 m, find the change in the mechanical energy due to friction. -7.0e4 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. J

Explanation / Answer

max distance spring comprssed apply energy conservation

loss in gravitational potential energy = gain in potential energy in spring

mgh = 1/2*k*x^2

14000*10 = 0.5* 1.6*10^6 *x^2

from this we got

x = 0.41833 m

force at his time = K*x = 1.6*10^6 * 0.41833

a = 1.6*10^6 * 0.41833 / ( 14000/9.81)

a = 469 m/s^2

part c

energy in in car = 14000*10 = 140000 J

energy in spring = 1/2* 1.6*10^6* 0.30^2 J

so loss in friction = 14000*10 -  1/2* 1.6*10^6* 0.30^2 = - 68000 J = - 6.8*e4 answer

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