An 8.0-kg box slides along a horizontal frictionless floor at 3 m/s and collides with a relatively massless spring that compresses 12 cm before the box comes to a rest. Calculate the retarding force of the spring.
Correct answer: C. 300N
- A. 3N
- B. 30N
- C. 300N
- D. 3000N
Explanation
m=8 kg, v=3 m/s, x=0.12 mFrictionless surfaceWe are asked for the retarding force of the spring.The spring force is not constant (it's F=kx), but the average force can be calculated from work done:Work done by spring=Kinetic energy of box Favg⋅x=1/2mv2Favg⋅0.12=1/2⋅8⋅32Favg⋅0.12=36 ⟹ Favg=36/0.12=300 N
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