The two crates are released from rest The two creates are released from rest. Th

Question

The two crates are released from rest The two creates are released from rest. Their masses are M_A = 4-kg and M_B = 20 kg, and the coefficient of kinetic friction between the crate A and the surface is mu_k = 0.3. (no friction on the pulley) (a) What is the acceleration of the crates? (b) Using the chain rule, find the velocity when crates moved 2m from the initial position. (c) Repeat (b) using the Energy Method. (d) What is the magnitude of the velocity of the crates after 2 s? (e) Repeat (d) using the Momentum Method.

Explanation / Answer

here,

Ma = 4 kg

Mb = 20 kg

uk = 0.3

a)

the accelration , a = ( Mb - uk * Ma) * g /( Ma + Mb)

a = ( 20 -0.3 * 4) * 9.81 /( 20 + 4)

a = 7.68 m/s^2

b)

when moved s = 2 m

the velocity , v = sqrt(2 * a * s)

v = sqrt(2 * 7.68 * 2) m/s

v = 5.54 m/s

c)

using conservation of energy

work done by frictional force = potential energy lost - kinetic energy gained

uk * Ma * g * s = Mb * g * s - 0.5 * ( Ma + Mb) * v^2

0.3 * 4 * 9.81 * 2 = 20 * 9.81 * 2 - 0.5 * ( 20 + 4) * v^2

solving for v

v = 5.54 m/s

d)

the magnitude of velocity after t = 2 s , v' = 0 + a * 2 = 15.36 m/s

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