springs and hooke’s law physics 11. springs a mass-spring system is given below. as mass is added...
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Springs and Hooke’s Law
Physics 11
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Springs
A mass-spring system is given below. As mass is added to the end of the spring, how would you expect the spring to stretch?
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Springs
mgFg
gmFg 1
gmFg 2
gmFg 3
x x
x
x
springg FF
springF
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Springs
2 times the mass results in a 2 times of the displacement from the equilibrium point…
3 time the mass… 3 times the displacement…
springg FF kxFspring
xkgm
kxmg
22
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What kind of energy is this?
Potential Energy Elastic Potential Energy to be exact!
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What else besides springs has elastic potential energy?
Diving boards Bows (bow and arrows) Bungee cord
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Hooke’s Law
Fspring: Applied force
X : displacement of the spring from the equilibrium position (units: m)
K: the spring constant (units: N/m)
kxFspring
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Hooke’s Law
the restoring force is opposite the applied force. (negative sign)
Gravity applied in the negative direction, the restoring force is in the positive direction
kxFspring
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Example
An archery bow requires a force of 133N to hold an arrow at “full draw” (pulled back 71cm). Assuming that the bow obeys Hooke’s Law, what is its spring constant?
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F = kx 133 = k(0.71) k = 133/0.71 k = 187.32 N/m 190 N/m
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Restoring Force
The restoring force is the force that is needed to put the spring back to equilibrium.
Example: If you stretch a spring by 0.5m and you had to use 150N of force, the restoring force is -150N.
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Practice Problems
Textbook Page 258
35-37
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Elastic Potential Energy of a Spring
Formula: Ee = ½ kx2
Units: Joules (J)
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Example:
A spring with spring constant 75 N/m is resting on a table.
A) If the spring is compressed a distance of 28cm, what is the increase in its potential energy?
B) What force must be applied to hold the spring in this position?
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Answer:
A) Ee = ½ kx2
Ee = ½ (75)(0.28)2
Ee = 2.9 J B) F = kx F= 75(0.28) F = 21 N
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Practice Problems
Page 261, questions 38, 39, 40 Page 261 (Section Review)
1, 2, 3, 4, 7
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Conservation of Energy with a Spring
Ex. 1: A 4.0 kg block slides across a frictionless table with a velocity of 5.0m/s into a spring with a stiffness of 2500 N/m. How far does the spring compress?
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Answer
X = 0.20m
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Example 2:
A 70. kg person bungee jumps off a 50.m bridge with his ankles attached to a 15m long bungee cord. Assume the person stops at the edge of the water and he is 2.0m tall, what is the force constant of the bungee cord?
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Answer: 64 N/m
Conservation of Energy Worksheet
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Practice Problems
Textbook Page 261
38-40 Section review (p 261)
1-10