Question

A 2.10-kg mass starts from rest at point A and moves along the x axis subject to the potential energy shown in the figure below.

30 J 25 J 20 J 15 J 10 J 5 J 2 m 4 m 6m 8m 10 m

(a) Determine the speed of the mass at points B, C, D.

B: _____ m/s

C: _____ m/s

D: _____ m/s

(b) Determine the turning points for the mass

Answer 1

a)
for point B
change in potential energy between A and B = 30-5 = 25 J
this must be equal to increase in kinetic energy
0.5*m*v^2 = 25
0.5*2.1*v^2 = 25
v = 4.88 m/s
Answer: 4.88 m/s

for point C
change in potential energy between A and C = 30-10 = 10 J
this must be equal to increase in kinetic energy
0.5*m*v^2 = 10
0.5*2.1*v^2 = 10
v = 3.09 m/s
Answer: 3.09 m/s

for point D
change in potential energy between A and D = 30-15 = 15 J
this must be equal to increase in kinetic energy
0.5*m*v^2 = 15
0.5*2.1*v^2 = 15
v = 3.78 m/s
Answer: 3.78 m/s

b)
V will be 0 at point E
at turning point v should be 0
so,
E is the turning point