(10 points) The spring and mass hanger with mass shown in the sketch is stretche

Question

(10 points) The spring and mass hanger with mass shown in the sketch is stretched from the equilibrium position C to the point labeled E and then released from rest. (Displacement is positive in the positive y direction shown.) The mass oscillates back and forth between positions of maximum (A), minimum (E) and zero (C) displacement.

(Since displacement goes below y=0, displacement can be negative. Similarly, velocity is positive going up and negative going down. Same for acceleration.)

1.  For what values of position (A, B, C, D and/or E) is the velocity of the mass largest?

2.  For what values of position (A, B, C, D and/or E) is the velocity of the mass smallest?

3.  For what values of position (A, B, C, D and/or E) is the acceleration of the mass greatest?

4.  For what values of position (A, B, C, D and/or E) is the acceleration of the mass the smallest?

5.  For what values of position (A, B, C, D and/or E) is the kinetic energy of the mass greatest?

7.  For what values of position (A, B, C, D and/or E) is the potential energy of the mass greatest?

8.  For what values of position (A, B, C, D and/or E) is the potential energy of the mass the smallest?

The spring and mass hanger with mass shown in the sketch is stretched from the equilibrium position C to the point labeled E and then released from rest. (Displacement is positive in the positive y direction shown.) The mass oscillates back and forth between positions of maximum (A), minimum (E) and zero (C) displacement. (Since displacement goes below y=0, displacement can be negative. Similarly, velocity is positive going up and negative going down. Same for acceleration.) For what values of position (A, B, C, D and/or E) is the velocity of the mass largest? For what values of position (A, B, C, D and/or E) is the velocity of the mass smallest? For what values of position (A, B, C, D and/or E) is the acceleration of the mass greatest? For what values of position (A, B, C, D and/or E) is the acceleration of the mass the smallest? For what values of position (A, B, C, D and/or E) is the kinetic energy of the mass greatest? For what values of position (A, B, C, D and/or E) is the kinetic energy of the mass the smallest? For what values of position (A, B, C, D and/or E) is the potential energy of the mass greatest? For what values of position (A, B, C, D and/or E) is the potential energy of the mass the smallest?

Explanation / Answer

1) C, as from C the spring opposes the motion velocity decreases, so velocity is latgest at C

2)A and E, at extremes velocity changes direction after coming to rest, so velocity is 0, so it is minumum at A and E.

3)A and E, force is greatest at these 2 points, so acceleration is greatest

4)C, force is 0 at C, so acceleration is minimum

5)C, velocity is highest, so KE is highest

6)A and E, velocoty is lowest, so KE is minimum

7) A, heighest point,so maximum PE

8) E, loewst point, so minimum PE

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