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Chapter 1: Q24E (page 265)

Block A in Fig E8.24 has mass 1.00 kg and block B has mass 3.00 kg. The blocks are forced together, compressing a spring S between them, then the system is released from rest on level, frictionless surface. The spring, which has negligible mass, is not fastened to either block and drops to the surface after it has expanded. Block B acquires a speed of 1.20 m/s. (a) What is the final speed of block A? (b) How much potential energy was stored in the compresses spring?

Short Answer

Expert verified

Thus, (a) the final speed of block A is 3.60 m/s.

(b) the potential energy stored in the compressed spring is 8.64 J

Step by step solution

01

Given in the question.

Mass of block A ism1=1.00kg

Mass of block B is m2=3.00kg

Final speed of block B is V2f=1.20m/s

Final speed of block A isv1f

02

the law of conservation of momentum.

The Law of conservation of momentum states that the total momentum of an isolated system remains conserved during any process.

03

(a) Obtain final speed of block A.

Apply the law of conservation of momentum as follows:

pi=pf0=m1v1f-m2v2fm2v2f=m1v1fv1f=m2v2fm1v1f=-3.00kg1.20m/s1kgv1f=3.60m/s

Hence, the final speed of block A is 3.60 m/s.

04

(b) Potential energy stored

Use the law of conservation of energy:

U=K1+K2=m1v1f22+m2v2f22=121kg脳3.60m/s2+3kg脳1.20m/s2=8.64J

Hence, the potential energy is 8.64 J .

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