Force & Tension: Does Length Matter?

[batballbat]

1. is it true that we have to apply lesser force in lifting a book by holding it near the center than by holding it at the end?

2. why isn't it easier to lift a weight attached to a string when the string is longer than when the string is shorter. is there a theoretical explanation?

 

[KingNothing]

1. is it true that we have to apply lesser force in lifting a book by holding it near the center than by holding it at the end?

2. why isn't it easier to lift a weight attached to a string when the string is longer than when the string is shorter. is there a theoretical explanation?

1) I am going to go ahead and rephrase this. "Is it true that it takes less work in lifting a book by holding it near the center than by holding it at the end?"

The answer is no. The amount of work done is equal to the change in gravitational energy. You can use any force you want; the amount of force (so long as it's greater than gravity) will only serve to accelerate the book faster or slower.

However, if you grab the edge and try to hold it straight, it may feel like you are doing work as you will be using the smaller muscles of your hand to balance it, and those muscles tend to exhaust more quickly under heavy load.

2) Why would it be easier to lift a weight attached with a longer string? If anything, it should be more difficult: you have to lift more string as well as the weight.

 

[Doc Al]

1. is it true that we have to apply lesser force in lifting a book by holding it near the center than by holding it at the end?

That depends on what you mean. The net force that you have to exert to lift an object (without acceleration) is always equal to the weight of the object regardless of where you hold it. But the actual forces exerted by parts of your hand may well vary with how you hold it.

To illustrate how the forces can vary, imagine holding a long wooden stick. Hold it in the middle. Your hand exerts some force on it. Now hold it by the very end. In order to hold it, your hand must exert a torque on the stick to keep it from twisting out of your grip. You'll end up pushing up with one part of your hand and down with another. Parts of your hand will be exerting forces greater than the weight of the stick. (That's why it's hard to hold it by the very end.) But the net force you must exert is still just equal to the weight of the stick.