a 160. kg crate, to the right of the pulley, is released from rest and begins to fall to the ground. If the crate accelerates at 4.45 m/s2, what is the mass of the block to the left of the pulley? Assume the rope and pulley are massless.
Question
a 160. kg crate, to the right of the pulley, is released from rest and begins to fall to the ground. If the crate accelerates at 4.45 m/s2, what is the mass of the block to the left of the pulley? Assume the rope and pulley are massless.
Solution
To solve this problem, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma).
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First, calculate the force of gravity acting on the crate. This is done by multiplying the mass of the crate by the acceleration due to gravity. Assuming the acceleration due to gravity is 9.8 m/s², the force of gravity (Fg) on the crate is:
Fg = mass_crate * g Fg = 160 kg * 9.8 m/s² Fg = 1568 N
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Next, calculate the net force acting on the crate. This is done by multiplying the mass of the crate by its acceleration. The net force (Fnet) is:
Fnet = mass_crate * a Fnet = 160 kg * 4.45 m/s² Fnet = 712 N
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The tension in the rope is equal to the difference between the force of gravity and the net force. So, the tension (T) is:
T = Fg - Fnet T = 1568 N - 712 N T = 856 N
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The tension in the rope is also equal to the weight of the block on the left side of the pulley. Therefore, we can find the mass of the block (mass_block) by dividing the tension by the acceleration due to gravity:
mass_block = T / g mass_block = 856 N / 9.8 m/s² mass_block = 87.35 kg
So, the mass of the block to the left of the pulley is approximately 87.35 kg.
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