One type of toy car contains a spring that is compressed as the wheels are rolle

Question

One type of toy car contains a spring that is compressed as the wheels are rolled backward along a surface. The spring remains compressed until the wheels are freed and the car is allowed to roll forward. Jose learns that if he rolls the car backward for a greater distance (up to a certain point), the car will go faster when he releases it. The spring compresses 1.00 cm for every 10.0 cm the car is rolled backward.

(a) Assuming the spring constant is 143.0 N/m, what is the elastic potential energy stored in the spring when Jose rolls the car backward 12.0 cm?
________ J

(b) What is the elastic potential energy stored in the spring when he rolls the car backward 41.0 cm?
_________ J

(c) Explain the correlation between the results for parts (a) and (b) and Jose's observations of different speeds.

Explanation / Answer

a)

Compressed distance is

X=12/10=1.2 Cm

the elastic potential energy stored in the spring is

E=(1/2)KX2=(1/2)*143*0.0122=0.0103 J

b)

X=41/10=4.1 cm

the elastic potential energy stored in the spring is

E=(1/2)KX2=(1/2)*143*0.0412=0.1202 J

c)

E1/E2=0.0103/0.1202=0.08566

Since E1/E2=(V1/V2)2

V1/V2=sqrt(0.08566)=0.2927

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