course Phy 231
June 285:18 pm
A rubber band begins exerting a tension force when its length is 8 cm. As it is stretched to a length of 10 cm its tension increases with length, more or less steadily, until at the 10 cm length the tension is 3 Newtons.
• Between the 8 cm and 10 cm length, what are the minimum and maximum tensions, and what do you think is the average tension?
F = kx
3 = k10
k = 0.3
F= 0.3 * 8 = 2.4 N
F = k x applies if F is a linear function of x, and x is measured relative to the equilibrium point.
The equilibrium point is not at x = 0, which would correspond to the rubber band being compressed to length 0.
The max force is 3 N and the min force is 2.4 N. Therefore the average tension should be 2.7 N.
• How much work is required to stretch the rubber band from 8 cm to 10 cm?
W = Fnet*d
W = 3*2 = 6 J
I'm not sure if this is right. I don't know which force to use, or how to find the net force in the situation.
• During the stretching process is the tension force in the direction of motion or opposite to the direction of motion?
The tension would be opposite the motion.
• Does the tension force therefore do positive or negative work?
That means the tension force does negative work.
The rubber band is released and as it contracts back to its 8 cm length it exerts its tension force on a domino of mass .02 kg, which is initially at rest.
• Again assuming that the tension force is conservative, how much work does the tension force do on the domino?
If we assume that the force is conservative, that I would assume that the force on the domino would be equal to the total work done found earlier, which is 6 J.
• Assuming this is the only force acting on the domino, what will then be its kinetic energy when the rubber band reaches its 8 cm length?
F = ma
3 = .02*a
a = 150 cm/s^2
v0 = 0
d= 2cm
.02 = 1/2 *150*t^2
.02 = 75t^2
t = .016 seconds
vf^2 = 2*150*8 = 49 cm/s
k = 1/2 mv^2
k = 1/2 * .02 * 24.5.^2
k = 6 J
• At this point how fast will the domino be moving?
The domino will be moving at 49 cm/s.
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I've commented more fully in a note appended to the document in the link below. You have some errors related to units, which gives you some incorrect results which, however, will be easy to correct since you understand the physics and the procedures.
&#You appear to understand, though there wasn't much detail in your work and self-critiques, so I can't be sure. Be sure to let me know if you have specific questions or points needing clarification. &#