In an experiment, a low-friction car with mass m = 0.400 kg is on a horizontal t

Question

In an experiment, a low-friction car with mass m = 0.400 kg is on a horizontal track. You can neglect friction. The cart is connected to a spring with force constant k = 4.90 N/m . You pull the cart away from the equilibrium point for the spring, stretching the spring 0.110 m , and then release it with no initial velocity. The cart moves back to its equilibrium position (x=0).

Part A

What is the speed of the glider when it returns to x=0?

Part B

What must the initial displacement of the glider be if its maximum speed in the subsequent motion is to be 2.70 m/s ?

Explanation / Answer

a)

By Conservation of energy

(1/2)KX2 ='(1/2)mV2

4.9*0.112=0.4*V2

V=0.385 m/s

b)

By Conservation of energy

(1/2)mV2 =(1/2)KX2

0.4*2.72 =4.9*X2

X=0.7714 m

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