Question 7

A 4 kg aluminum block hangs as a pendulum on a string two meters long as shown in Fig. A. Its period is T0 . A 0.01 kg lead bullet is fired into the block and becomes embedded there as shown in Fig. B. The block swings through a vertical displacement of 0.27 meters as shown in Fig. C.

  • (a) What is the tension in the string before the bullet is fired? (Let g = 10 m/s2 )
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  • (b) What is the tension in the string after the pendulum has reached its maximum displacement? (Fig. C)
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  • (c) What is the recoil speed of the block + bullet? (Fig. B)
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  • (d) What is the initial speed of the bullet? (Fig. A)
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  • (e) What is the tension in the string just after the bullet stops in the aluminum block? (Fig.B) Hint: block now moving in a circle.
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  • (f) What is the torque on the pendulum about point O at this instant?
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  • (g) What is the angular momentum of the pendulum about point O at this instant?
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  • (h) What is the torque about point O, when the pendulum has reached its maximum displacement? (Fig. C)
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  • (i) What is the angular momentum about point O, when the pendulum has reached maximum displacement? (Fig. C)
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  • (j) Is the angular momentum about point O of the system of block + bullet conserved?
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  • (k) From conservation of total energy, how many kcal of heat are developed in the (block + bullet) system?
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  • (l) What is the temperature change of the (block + bullet) system? Specific heat capacity of Al is 0.21 cal/g*K).
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  • (m) The period of this pendulum after the bullet is embedded is (greater than, equal to, less than) the period of the pendulum, T0 , before the bullet is fired.
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