A 2.0-kg cart and an 8.0-kg cart are connected by a relaxed, horizontal spring o

Question

A 2.0-kg cart and an 8.0-kg cart are connected by a relaxed, horizontal spring of spring constant 300 N/m. You pull the 8.0-kg cart with some constant horizontal force. The separation between the carts increases for a short time interval, then remains constant as you continue to pull and the spring is stretched by 0.100 m.

part A

What pulling force did you exert? Assume that the direction of your pull is the positive direction. Express your answer to two significant figures and include the appropriate units.

part B

If you instead pull the 2.0-kg cart, what force must you exert to get the same stretch in the spring? Assume that the direction of your pull is the positive direction. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

a)Let the force be F.

Tension in the spring=kx=300*0.1=30N

Acceleration of the system=30/2=15m/s^2

F=ma=10*15=150N

b)For the same extension in the spring, T=30N

acceleration of the 8 kg mass=acceleration of the system=30/8=3.75m/s^2

F=10*3.75=38N

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