A 14,000 N car starts from rest and rolls down a hill from a height of 10.0 m (s

Question

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.

EXERCISE

A spring-loaded gun fires a 0.090-kg puck along a tabletop. The puck slides up a curved ramp and flies straight up into the air.

(a) If the spring is displaced 23.5 cm from equilibrium and the spring constant is 875 N/m, how high does the puck rise, neglecting friction?
x = _______ m

(b) If instead it only rises to a height of 5.00 m because of friction, what is the change in mechanical energy?
Wnc = _____ J

Explanation / Answer

Using Work Eneergy principle:

All the gravitational PE stored at the top is converted to spring PE at the bottom.

So, mgh = 0.5*k*x^2 <---------- x = maximum compression of the spring

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

So, x = 0.418 m <------ answer

b)

Maximum acceleration, a = kx/m = 1.6*10^6*0.418/(14000/9.8)

= 468.2 m/s2 <------ answer

c)

Change in Mechanical energy due to friction = mgh - 0.5*k*x^2

= 14000*10 - 0.5*1.6*10^6*(0.3)^2

= -68000 J

EXERCISE :

a)

All the PE stored in the spring is converted to gravitational PE .

So, 0.5*k*x^2 = mgh

So, 0.5*875*(0.235)^2 = 0.09*9.8*h

So, h = 27.4 m <------- answer

b)

Change in mechanical energy due to friction = 0.5*k*x^2 - mgh

= 0.5*875*0.235^2 - 0.09*9.8*5

= -19.8 J <------- answer

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