Frictionless pulley system
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Frictionless pulley system
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[post_date] => 2025-01-09 07:31:06
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
A 3kg box on a frictionless table is connected to another hanging 5kg black circular mass via a massless string and a frictionless pulley as seen below.
After the 3kg mass and the 5kg mass are released from rest, they move with constant acceleration. It takes 0.808 seconds for the hanging 5kg black mass to fall 2m and hit the floor. After the 5kg mass hits the floor the string goes slack and no longer exerts any force on either mass.
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[question] => What is the magnitude of the acceleration of the 3kg box while it moves through the first 2m of motion?
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[answer] => 1
[description] => Reason for the Correct Answer:
Since the acceleration is constant, the kinematic formulas can be applied. And since the masses are connected, the acceleration of the 5kg mass is the same as the acceleration of the 3kg mass.
The 5kg mass starts from rest so it has an initial velocity of zero, and it takes 0.808 seconds to move 2m
Use the formula Δx= vₒt + ½ at²
Plug in vₒ=0, t=0.808 seconds, and Δx=2m into the formula Δx= vₒt + ½ at² to get a=6.13m/s²
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[answers] => Array
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[0] => Array
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[each_answer] => A. 6.13 m/s²
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[1] => Array
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[each_answer] => B. 4.28 m/s²
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[2] => Array
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[each_answer] => C. 4.28 m/s²
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[3] => Array
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[each_answer] => D. 4.28 m/s²
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => After the 3kg mass flies off the end of the table and is moving through the air, what is the net force exerted on the 3kg mass? (ignore air resistance)
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[answer] => 2
[description] => Reason for the Correct Answer:
As the 3kg mass flies through the air it is affected only by the force of gravity since the string has gone slack.
The force of gravity near the surface of the Earth is given by Fᵍ= mg.
The force of gravity is equal to 3kg x 9.8m/s² = 29.4 N. Since this is the only force acting on the object, it is also the net force on the object.
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[answers] => Array
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[0] => Array
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[each_answer] => A. 0 N
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[1] => Array
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[each_answer] => B. 29.4 N downwards
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[each_answer] => C. 24.7 N to the left
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[3] => Array
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[each_answer] => D. 18.6 N to the right
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => What is the acceleration of the 3kg mass right after the 5kg mass hits the floor?
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[answer] => 4
[description] => Reason for the Correct Answer:
Think about Newton’s First Law.
Newton’s First Law says that objects will maintain constant velocity unless acted on by an external force.
After the 5kg mass hits the ground, the tension will drop to zero, which means there will no longer be a horizontal force on the 3kg mass. No force means no acceleration so the acceleration of the 3kg mass will be zero after the 5kg mass hits the ground.
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[answers] => Array
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[0] => Array
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[each_answer] => A. 2.97 m/s²
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[each_answer] => B. 6.13 m/s²
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[each_answer] => C. 9.8 m/s²
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[each_answer] => D. 0 m/s²
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[quiz_unique_key] => 2261298308
[question] => Imagine resetting the experiment, except you replace the black 5kg mass with a 1 kg mass. If you let go of the 1kg mass from rest, how would the masses move?
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[answer] => 2
[description] => Reason for the Correct Answer:
The table is frictionless.
Since the table is frictionless, the only horizontal force on the 3kg mass will be the tension in the string.
Since the 1kg mass will cause tension in the rope, and the tension is the only horizontal force on the 3kg mass, the masses will have to accelerate.
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[answers] => Array
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[0] => Array
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[each_answer] => A. The masses would not move since the 1kg mass will not have enough force to overcome the gravitational force on the 3kg mass
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[each_answer] => B. The masses would start to accelerate, but with an acceleration less than when the 5kg mass was attached
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[each_answer] => C. The masses would not start moving because the 1kg mass would not cause any tension in the rope
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[each_answer] => D. The masses would start to move, but would not accelerate
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[quiz_unique_key] => 2261298308
[question] => What is the tension in the string?
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[answer] => 1
[description] => Reason for the Correct Answer:
Use ΣF = ma for the horizontal forces on the 3kg mass.
The only horizontal force on the 3kg mass is the tension from the string.
The 5kg mass starts from rest so it has an initial velocity of zero, and it takes 0.808 seconds to move 2m.
Using the formula ∆x = vₒt + ½ at² , you can plug in vₒ = 0, t = 0.808 sec, and ∆x = 2m into the formula ∆x = vₒt + ½ at² to get a = 6.13m/s²
Plugging the value for acceleration into the formula ΣF = ma, you get T = 3kg x 6.13m/s² = 18.4 N
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[answers] => Array
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[0] => Array
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[each_answer] => A. 18.4 N
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[each_answer] => B. 49.0 N
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[2] => Array
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[each_answer] => C. 14.6 N
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[each_answer] => D. 29.4 N
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