Oscillating graphs A mass is hanging from a spring off the edge of a table. The

Question

Oscillating graphs A mass is hanging from a spring off the edge of a table. The position of the mass is measured by a sonic ranger sitting on the floor 25 cm below the mass's equilibrium position. At some time, the mass is started oscillating. At a later time, the sonic ranger begins to take data. Below arc shown a series of graphs associated with the motion of the mass and a scries of physical quantities. The graph labeled (A) is a graph of the mass's position as measured by the ranger. For each physical quantity identify which graph could represent that quantity for this situation. If none arc possible, answer N. Briefly explain each answer. velocity of the mass net force on the mass force exerted by the spring on the mass kinetic energy of the mass potential energy of the spring gravitational potential energy of the mass

Explanation / Answer

1) B velocity will alternate between positive and negative as the mass move up and down. starts positive .

2) C F=ma as the acceleration is constantly changing, and it will be zero when velocity is at it's highest point, it will be 'opposite' to the velocity graph. starts negative as the mass is slowing down

3) D Fs=k dX where k is the spring constant. when the mass is in the original position, dX =0 so F=0. can never be negative because the spring is eventually compressed as far as phyically possible.

4) E KE=1/2 *m *V^2 as V is squared, KE is always positive as well. and will oscillate twice as fast as the force graph.

5)     PE=1/2 * k * x^2    assuming the low points on the position graph are when the mass is closest to the sensor, and the spring is stretched out, then the energy in the spring would be greatest at these points. The curve would peak around 2 and 5 seconds. None seem possible

6) F PE =mgh curve looks like position graph. But it is never 0 as it never touches the ground.

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