A 20-kg crate hangs at the end of a long rope. Find its acceleration (magnitude and
direction) when the tension in the rope is (a) 250 N, (b) 150 N, (c) zero, (d) 196 N.
(a)
The magnitude of the acceleration on thecrate when
Answer to Problem 57SP
Solution:
Explanation of Solution
Given data:
The mass of the crate is
The tension force in the rope is
Formula used:
FromNewton’s second law of motion, the expression of the sum of the force acting upon the crateis as follows:
Here,
Explanation:
Draw the free body diagram of the crate:
Here,
Recall the expression for Newton’s second law of motion when the motion of the crate is along the vertical direction:
Considering the direction of the forces, upward is taken aspositive and downward direction of the forces is taken as negative. Hence,
Rearrange the value for acceleration, a, of the crate:
Substitute
Conclusion:
Therefore, the acceleration on the crate is
(b)
The magnitude of the acceleration on the crate when
Answer to Problem 57SP
Solution:
Explanation of Solution
Given data:
Mass of the crate that is hanging is
Tension force is
Formula used:
From Newton’s second law of motion, the expression of the sum of the force acting upon the crateis as follows:
Here,
Explanation:
Draw the free body diagram of the crate:
Here,
Recall the expression for Newton’s second law of motion:
Considering the direction of the forces, upward is taken as positive and downward direction of the forces is taken as negative. Hence,
Rearrange the value for acceleration a:
Substitute
Here, the value of
Conclusion:
The acceleration on the crate is
(c)
The magnitude of the acceleration on the crate when
Answer to Problem 57SP
Solution:
Explanation of Solution
Given data:
Mass of the crateis
Tension force in the rope is
Formula used:
From Newton’s second law of motion, the expression of the sum of the force acting upon the rope is as follows:
Here,
Explanation:
Draw the free body diagram of the crate:
Here,
Recall the expression for Newton’s second law of motion:
Considering the direction of the forces, upward is taken as positive and downward direction of the forces is taken as negative. Hence,
Rearrange the value for acceleration a:
Substitute
The negative value of
Conclusion:
The acceleration on the crate is
(d)
The magnitude of the acceleration on the crate when
Answer to Problem 57SP
Solution:
Explanation of Solution
Given data:
The mass of the crateis
The tension force in the rope is
Formula used:
From Newton’s second law of motion, the expression of the sum of the force acting upon the rope is as follows:
Here,
Explanation:
Draw the free body diagram of the crate:
Here,
Recall the expression for Newton’s second law of motion:
Considering the direction of the forces, upward is taken as positive and downward direction of the forces is taken as negative. Hence,
Rearrange the value for acceleration of the crate:
Substitute
Conclusion:
The acceleration on the crate is
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Chapter 3 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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