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Figure 8-36a applies to the spring in a cork gun (Fig. 8-36b): it shows the spring force as a function of the stretch or compression of the spring. The spring is compressed by 6.0 cm and used to propel a 3.8 g cork from the gun. Force (N) 0.4 0.2 22 4X (cm) Cork Compressed spring INNE Figure 8-36. (a) What is the speed of the cork if it is released as the spring passes through its relaxed position? 3.07 m/s (b) Suppose, instead, that the cork sticks to the spring and stretches it 1.5 cm before separation occurs. What now is the speed of the cork at the time of release? x m/s



Answer :

The calculated value is 2.7 m/s. The graph's slope allows us to determine the spring constant, k=x. F = 0.10 N/cm = 10 N/m.

(a) By equating the compressed spring's potential energy to the cork's kinetic energy during release, we arrive at

2 1 kx 2 equals 2 1 mv 2, where v=x m k.

​which results in a speed of 2.8 m/s for

m=0.0038 kg and

x=0.055 m.

(b) The new scenario entails the release of some potential energy. Conservation of energy changes when d=0.015m

2 1 kx 2

= 2 1 mv 2 + 2 1 kd 2 v

= m k (x 2 d 2)

​resulting in v=2.7 m/s.

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