(a)
The work required to lift the box.
(a)
Answer to Problem 6SP
The work required to lift the box is
Explanation of Solution
Given info: The weight of the box is
Write the expression for work done when force applied force and the displacement are in the same direction.
Here,
Since the weight of the box is
Substitute
Conclusion:
Therefore, the work required to lift the box is
The amount of work required to push the box up the ramp.
Answer to Problem 6SP
The amount of work required to push the box up the ramp is
Explanation of Solution
Given info: The length of the ramp is
Since the component of the weight (gravitational force) along the ramp is
Substitute
Conclusion:
Therefore, the amount of work required to push the box up the ramp is
(c)
Which among the situations, pushing up the ramp or lifting straight up required more work.
(c)
Answer to Problem 6SP
The amount of work required for both pushing up the ramp and lifting straight up are the same.
Explanation of Solution
The word work defines an activity involving mental or physical health but in physics it is defined as the force causing movement or displacement of an object. The SI unit of work is Joule.
If the force and distance moved are in same direction, then the work is the applied force multiplied by the distance object moves. The work done by a given force is the product of the component of the force along the line of motion of the object multiplied by the distance that the object moves under the influence of the force.
From part (a) it is obtained that the work required to lift the box straight up is
Conclusion:
Therefore, the amount of work required for both pushing up the ramp and lifting straight up are the same.
(d)
Which among the situations, pushing up the ramp or lifting straight up requires more force.
(d)
Answer to Problem 6SP
Lifting the box straight up requires more force than pushing it up the ramp.
Explanation of Solution
The capacity to make a physical change or to do work is known as force. The work done by a given force is the product of the component of the force along the line of motion of the object multiplied by the distance that the object moves under the influence of the force.
Since the gravitational force over the box is
Conclusion:
Therefore lifting the box straight up requires more force than pushing it up the ramp.
(e)
Which among the situations, pushing up the ramp or lifting straight up, the distance moved is greater.
(e)
Answer to Problem 6SP
The distance moved is greater in pushing the box up the ramp than that in lifting the box straight up.
Explanation of Solution
The word work defines an activity involving mental or physical health but in physics it is defined as the force causing movement or displacement of an object.
By definition, the work done by a force is equal to the product of force and the displacement of the object in the direction of application of force. If work done in two situations are equal, the situation in which more force is applied will have smaller displacement of the object on which the force is acting.
In both the given situations, the work done is same. From part (d) the force required is greater in lifting the box straight up. This implies force is applied over a long distance when the box is pushed up the ramp.
Conclusion:
Therefore the distance moved is greater in pushing the box up the ramp than that in lifting the box straight up.
(f)
The change in the gravitational potential energy of the box for lifting the box straight up and pushing it up the ramp.
(f)
Answer to Problem 6SP
The change in the gravitational potential energy of the box for lifting the box straight up and pushing it up the ramp is
Explanation of Solution
Given info: The height of the final position of the box is
Since the same box is considered in both the situations, the mass is same.
Write the expression gravitational force on the object.
Here,
Substitute
Write the expression for the change in gravitational potential energy.
Here,
Since in both processes, the box is moved from the initial ground level to a final height of
Substitute
Thus, the change in the gravitational potential energy of the box for lifting the box straight up and pushing it up the ramp is
Conclusion:
Thus the change in the gravitational potential energy of the box for lifting the box straight up and pushing it up the ramp is
(g)
The advantage of using the ramp to move the box.
(g)
Answer to Problem 6SP
When the ramp is used to move the box to the given height, less force is required than lifting it straight up to the height and hence the strength of the person doing work can be conserved using the ramp.
Explanation of Solution
Work defines an activity involving mental or physical health but in physics it is defined as the force causing movement or displacement of an object. The work done by a given force is the product of the component of the force along the line of motion of the object multiplied by the distance that the object moves under the influence of the force.
When the box has to be lifted straight up, the person has to work against the complete gravitational attraction on the box or against the weight of the box. But when ramp is used work has to be done against only the component of the weight of the box along the ramp.
As obtained in the calculations, the force required to move the box to the final position is
Conclusion:
Thus when the ramp is used to move the box to the given height, less force is required than lifting it straight up to the height and hence the strength of the person doing work can be conserved using the ramp.
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