1) A 15 cm long spring is attached to the ceiling. When a 2.2 kg mass is hung fr

Question

1) A 15 cm long spring is attached to the ceiling. When a 2.2 kg mass is hung from it, the spring stretches to a length of 20 cm.

(a) What is the spring constant k?

(b) How long is the spring when a 3.0 kg mass is suspended from it?

2) To tighten a bolt, you push with a force of 100 N at the end of a wrench handle that is 0.25 m from the axis of the bolt.

(a) What torque are you exerting?

(b) If you move your hand inward to be only 0.15 m from the bolt, what force do you have to exert to achieve the same torque?

Explanation / Answer

1)

for a spring:

F = kx

F = mg = (2.2)(9.81) = 21.58 N

k = F/x = 21.58/0.05 = 431.64 N/meter
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(b)

delta x = F/k = mg/k = (3)(9.81)/392.4 = 0.068 meters

Length of spring = 0.068 + 0.15 = 0.218 meters

2)

a)
Torque is the same as moment about a point.. r x F is the definition of torque about a point. F= 100N and

r = perpendicular distance from the force to the point..

so 100 times .25m = 25Nm

(b) Force = F=?

distance = r =0.15 m

torque = t = r*F= 25 Nm

F = 25/r = 25/0.15= 166.66 N = 167N

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