Shown here is the graph of the total potential energy of an 8-kg mass as it move

Question

Shown here is the graph of the total potential energy of an 8-kg mass as it moves only along one axis (call it the r-axis). Its velocity along this axis, vr, is (+)2.00 m/s when it is located at r = 8.00 m. No external work is done on the mass.

Evaluate (T/F/N) each statement below, and don

Shown here is the graph of the total potential energy of an 8-kg mass as it moves only along one axis (call it the r-axis). Its velocity along this axis, vr, is (+)2.00 m/s when it is located at r = 8.00 m. No external work is done on the mass. Evaluate (T/F/N) each statement below, and don't forget to explain your reasoning and justify each answer. (i) The mass does not achieve the position of r = 14.0 m. At r = 9.00 m, Fnet.r is exerted in the negative r-direction. At r = 3.00 m, ar = (+)5.00 m/s2.

Explanation / Answer

1) KE at r = 8 m will be m*v*v/2 = 16 J

PE = 60 J

Since, force is conservative . Total energy is conserved.

Energy at r=14 is 160 which is not possible. Hence, it will not go to r = 14 m

2) False.

In a conservative system, F = -dU/dr

dU/dr is slope which is negative at r=9. Hence, force must be +ve.

3) F = -dU/dr

so at r = 3 m

dU/dr = -160/4 = -40 N

F = 40 N

acc = 40/8 = 5m/s2

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