Two crates of mass m1 = 44 kg and m2 = 16 kg are connected by a massless rope th
ID: 1977852 • Letter: T
Question
Two crates of mass m1 = 44 kg and m2 = 16 kg are connected by a massless rope that passes over a massless, frictionless pulley as shown in the figure below. The crates start from rest.
(b) What are the initial kinetic and potential energies of each crate? (Use the following as necessary: h for the distance from the bottom of m2 to the bottom of m1.)
PE1i =
KE1i =
PE2i =
KE2i =
(c) If the crate on the left (m1) moves downward through a distance h, what is the change in the potential energy of m1 and m2? Express your answers in terms of h.
PE1 =
PE2 =
(d) What is the speed of the crates after they have moved a distance h = 2.6 m?
v =
wo crates of mass m1 = 44 kg and m2 = 16 kg are connected by a massless rope that passes over a massless, frictionless pulley as shown in the figure below. The crates start from rest. (b) What are the initial kinetic and potential energies of each crate? (Use the following as necessary: h for the distance from the bottom of m2 to the bottom of m1.) PE1i = KE1i = PE2i = KE2i = (c) If the crate on the left (m1) moves downward through a distance h, what is the change in the potential energy of m1 and m2? Express your answers in terms of h. Delta PE1 = Delta PE2 = (d) What is the speed of the crates after they have moved a distance h = 2.6 m? v =Explanation / Answer
Given that mass m1= 44 kg
mass of the second crate m2 = 16 kg
Initially they are seperated by a distance h
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(a) The potential energy of the first crate
PE1i = m1gh = (44 kg)(9.8 m/s2)(h)
= 431.2 h J
Since initially the system is at rest
Kinetic energy of the first crate is KE1i = 0
Potential energy of the second crate PE2i = 0
kinetic energy of the second crate KE2i = 0
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(b) The change in potential energy of masses
Potential energy of first mass
PE1f = 0
and potential energy of second mass is
PE2f = m2gh = (16 kg)(9.8 m/s2)(h)
= 156.8 h J
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(c) From law of conservation of energy
m1gh = m2gh + 1/2 m1v12 + 1/2 m2v22
Since the total system has same speed.
431.2 (2.6 m) = (156.8)(2.6 m) + (0.5)(44 kg + 16 kg) v2
v2 = (431.2 - 15.68 )(2.6 m) / (0.5)(60 kg)
Therefore the speed of the crates
v = 4.87 m/s or 5 m/s
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