Concept explainers
A 60-kg crate is lowered from a loading dock to the floor using a rope passing over a fixed support. The rope exerts a constant upward force on the crate of 500 N.
- a. Will the crate accelerate? Explain.
- b. What are the magnitude and direction of the acceleration of the crate?
- c. How long will it take for the crate to reach the floor if the height of the loading dock is 1.4 m above the floor?
- d. How fast is the crate traveling when it hits the floor?
(a)
Whether the crate will accelerate.
Answer to Problem 4SP
The crate will accelerate downward since there is a net force acting in the downward direction.
Explanation of Solution
Given info: The mass of the crate is
Write the expression for the gravitational force.
Here,
Substitute
This force acts in the downward direction.
Write the expression for the net force.
Here,
The negative sign indicate that upward force is opposite to gravitational force.
Substitute
The net force is
Therefore according to the newton’s second law there will be a downward acceleration for the crate.
Conclusion:
Thus, the crate will accelerate downwad since there is a net force acting in the downward direction.
(b)
The magnitude and direction of acceleration.
Answer to Problem 4SP
The magnitude and direction of acceleration is
Explanation of Solution
Given info: The mass of the crate is
Write the expression for the acceleration of the crate.
Substitute
The direction is downward.
Conclusion:
Thus, the magnitude and direction of acceleration is
(c)
The time taken by the crate to reach the floor, if the crate is
Answer to Problem 4SP
The time taken by the crate to reach the floor, if the crate is
Explanation of Solution
Given info: The distance is
Assume that the crate is rest initially.
Write the expression for the distance travelled by the block.
Here,
Substitute
Conclusion:
Thus, the time taken by the crate to reach the floor, if the crate is
(d)
The velocity of the crate when it hits the floor.
Answer to Problem 4SP
The velocity of the crate when it hits the floor is
Explanation of Solution
Write the expression for the velocity of the crate.
Substitute
Conclusion:
Thus, the velocity of the crate when it hits the floor is
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Chapter 4 Solutions
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