A massless pulley connects to masses m1=6000kg and m2=11000kg. The string connec

Question

A massless pulley connects to masses m1=6000kg and m2=11000kg. The string connecting them is assumed to be massless and frictionless as well. In part (a) of the figure, the two masses are at rest and at the same height y = 0 y=0. Choosing the gravitational potential energy to be U ( y ) = m g y U(y)=mgy,

(a) calculate the total potential energy of the two masses

(b) Compute the total mechanical energy (i.e. the sum of kinetic plus potential energy for both masses):

(c) In part (b) of the figure, the masses have moved so that m1 has displaced vertically up by a distance of h=0.15m which implies that m2 has gone down to a position y=-h. Calculate the potential energy of the two masses now:

(d) Using conservation of energy, Calculate the total kinetic energy

(e) What is the ratio of the speeds (not velocities!) of the two masses in figure(b)?

(f) Using the definition of kinetic energy and the answer to part (e), calculate what the final speed is of m1

Explanation / Answer

a)

Utotalinitial = m1 gy + m2 gy = (6000 + 11000) (9.8) (0) = 0 J

b)

Total mechanical energy = Utotalinitial + KEtotalinitial= 0 + 0 = 0 J

c)

Utotalfinal = m1 gy + m2 gy = (6000) (9.8) (h) - (11000) (9.8) (h) = (6000) (9.8) (0.15) - (11000) (9.8) (0.15) = - 7350 J

d)

Total initial mechanical energy = total final mechanical energy

0 = Utotalfinal + KEfinal

0 = - 7250+ KEfinal

KEfinal = 7250 J

e)

Ratio = 1

the two masses are connected by same string , hence they move at same speed.

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