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Acceleration along a pulley with a ledge
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I have the 6th edition, which has that as problem 4-81. The answers seem OK to me.(That answer in your book must be a typo or something.)In summary, the conversation involves solving a problem using the equation F = ma, where the solution is 1.12m/s^2. However, there is confusion about the direction and magnitude of the acceleration for the masses involved, specifically the 20kg mass and the other mass. Through discussion and re-evaluation, it is determined that the acceleration of the second mass must be twice the acceleration of the first, resulting in an answer of 2.45m/s^2, which is consistent with other sources. The discrepancy in the answer provided
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Doc Al
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Hint: Do the masses have the same acceleration?
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fontseeker
They do, so that is why I am treating acceleration with the same variable for both. The answer book says they have the same acceleration but in different direction, but the magnitude should be the same.Doc Al said:
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Rethink that. If the 20 kg mass moves 1 m to the right, how far does the other mass move down? (Consider the string.)fontseeker said:
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fontseeker
0.5m down. However, that means that they are both positive then? However, I don't know how to prove it, it just makes sense since the tension is twice as much on the 20kg object.Doc Al said:
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Doc Al
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No. If the 20 kg mass moves 1 m to the right, how much rope must have passed over the pulley?fontseeker said:
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fontseeker
One meter would have had to pass.Doc Al said:
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Doc Al
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Nope. Draw yourself a quick picture of before and after and measure the length of the string that must have passed. (Or grab an actual piece of string and try it.)fontseeker said:
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fontseeker
Ah okay, since it is moving to the right 1 meter, 1 meter at the top and 1 meter at the bottom are loose, meaning 2 meters down.Doc Al said:
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Doc Al
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Good! So how must the accelerations of the two masses relate to each other?fontseeker said:
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fontseeker
The acceleration of the second block would be twice the acceleration of the first.Doc Al said:
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Doc Al
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Exactly. Now rewrite your equations with that in mind.fontseeker said:
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Doc Al
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That's the correct answer for the acceleration of the 20 kg mass.fontseeker said:
That answer makes no sense for this problem. What book is this?fontseeker said:
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fontseeker
TiplerDoc Al said:
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Doc Al
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I have the 6th edition, which has that as problem 4-81. The answers seem OK to me.fontseeker said:
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Doc Al
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(That answer in your book must be a typo or something.)
FAQ: Acceleration along a pulley with a ledge
How does a pulley affect acceleration?
A pulley can affect acceleration by changing the direction of the applied force. If the force is applied downward on one end of the rope, the object being lifted will experience upward acceleration due to the tension in the rope. This allows for heavier objects to be lifted with less force, making work easier.
What is the difference between acceleration and velocity?
Acceleration is the rate of change of velocity. Velocity is the speed and direction of an object's motion. So, while velocity tells us how fast an object is moving and in what direction, acceleration tells us how much the velocity is changing over time.
How does a ledge affect the acceleration along a pulley?
A ledge can affect the acceleration along a pulley by adding an additional force acting on the object. This force can either increase or decrease the acceleration depending on the direction and magnitude of the force. If the ledge is smooth, it may decrease the acceleration as it reduces friction. However, if the ledge is rough, it may increase the acceleration due to the added friction.
Can the mass of the object being lifted affect acceleration along a pulley with a ledge?
Yes, the mass of the object being lifted can affect the acceleration along a pulley with a ledge. Heavier objects require more force to be lifted, which can affect the acceleration. Additionally, the mass of the object can also affect the tension in the rope, which can further impact the acceleration.
How does the angle of the rope affect acceleration along a pulley with a ledge?
The angle of the rope can affect the acceleration along a pulley with a ledge by changing the direction and magnitude of the force acting on the object. As the angle increases, the horizontal component of the force decreases, resulting in a decrease in acceleration. However, the vertical component of the force increases, which can increase the tension in the rope and affect the acceleration.