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Problem Number 1From the length and mass of a simple pendulum we determine that the restoring force constant is k = m g / L. A bullet of mass 50 grams and moving at unknown velocity is quickly absorbed into the 6.1 kg mass of the pendulum, which is initially at rest. The pendulum absorbs the bullet, and its mass is observed to move to a maximum displacement of .086 meters from the equilibrium position.
Find the velocity of the mass immediately after absorbing the bullet, and the velocity of the bullet immediately before impact. Assume that no dissipative forces act on the system after the collision.
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Problem Number 2What is the centripetal acceleration, in m/s ^ 2, of the reference point on the circle which models the vertical simple harmonic motion of a mass of 7.7 kilograms, released from rest at a distance of .55 meters from its equilibrium position, when a restoring force of 100 Newtons/meter acts to pull the object back to its equilibrium point?
What acceleration would you expect for the object at the instant it reaches an extreme point?
Explain in your summary why you would expect the object itself to undergo this acceleration at the extreme positions in its cycle.
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Problem Number 3If a force vector has x and y components -5.7 Newtons and 6 Newtons, respectively, the what are the magnitude and angle the vector?
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Problem Number 4An object is pushed a distance of 18 meters by a force of 4 Newtons, with the force in the direction of the displacement.
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Problem Number 5The restoring force for a pendulum, when the displacement of the pendulum from its equilibrium position is small compared to its length, is in the same proportion to its weight as its displacement from equilibrium is to its length.
Recompute for a pendulum of the same length, but with a mass of your choosing.
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Problem Number 6An ideal spring has restoring force constant 980 Newtons/meter. An unknown mass on the spring is observed to complete 60.6 cycles every minute. What is the unknown mass, in kilograms?
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Problem Number 7The kinetic energy of an object is equal to the work required of the net force to accelerate it from rest to its present velocity. It is easily enough shown that this work is equal to .5 m v^2, where m is the mass and v the velocity of the object. This quantity is independent of the acceleration. We therefore say that the kinetic energy of the object is .5 m v^2.
If an object of mass 94 kg is moving at 2 m/s, what is its KE?
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Problem Number 8The velocity of an observed object increases at a rate of 9 m/s per second. The object is observed for 8 seconds.
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Problem Number 9An object of mass 11 kg is subjected to a variable force F(t) (here F(t) indicates function notation, not multiplication of F by t; F(t) is the force at clock time t) for .8 seconds.
During the .8-second time interval, the force increases linearly from 0 to 77 Newtons, then decreases linearly back to 0.
Find the change in the object's velocity.
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Problem Number 10A piece of magnetic metal, initially stationary, is being pulled by two different magnets. The first pulls with a force of 2.67 pounds to the North and the second with a force of 3.43 pounds to the East. The object starts to move in response to the combined force.
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Problem Number 11An object moving to the right at 5 m/s collides with an object moving at -5 m/s (i.e., to the left). The mass of the first object is 4 kg and the mass of the second is 5 kg.
After the collision, which lasts .065 seconds, the first object is observed to have velocity -5 m/s (this negative velocity is toward the left). .
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Problem Number 12 The velocity of an object increases by 24 meters per second during its lifetime.