Concept explainers
Determine the work of the force when it displaces 2 m.
a)
The work of a force.
Answer to Problem 1PP
The work done by the force on the block is
Explanation of Solution
Given:
The force acting on the block is
The displacement of the block is
Draw the free body diagram of block as shown in Figure (a).
Write the formula for work done force
Here,
Conclusion:
Refer Figure (a).
Resolve the force along
Substitute
Thus, the work done by the force on the block is
b)
The work of a force.
Answer to Problem 1PP
The work done by the force on the block is
Explanation of Solution
Given:
The force acting on the block is
The displacement of the block is
Draw the free body diagram of block as shown in Figure (b).
Write the formula for work done force
Here,
Conclusion:
Refer Figure (1).
The force acting on the block does not cause any displacement of the block. Hence the work done by the force is zero.
Thus, the work done by the force on the block is
c)
The work of a force.
Answer to Problem 1PP
The work done by the force on the block is
Explanation of Solution
Given:
The force acting on the block is
The displacement of the block is
Draw the free body diagram of block as shown in Figure (c).
Write the formula for work done force
Here,
Conclusion:
Refer Figure (c).
Substitute
Thus, the work done by the force on the block is
d)
The work of a force.
Answer to Problem 1PP
The work done by the force on the block is
Explanation of Solution
Given:
The force acting on the block is
The displacement of the block is
Draw the free body diagram of block as shown in Figure (d).
Write the formula for work done force
Here,
Conclusion:
Refer Figure (d).
Resolve the force along
Substitute
Thus, the work done by the force on the block is
e)
The work of a force.
Answer to Problem 1PP
The work done by the force on the block is
Explanation of Solution
Given:
The displacement of the block is
The given
Draw the free body diagram of block as shown in Figure (1e).
The graph consists of two geometrical cross sectional areas namely triangle and rectangle.
Write the formula for work done force
Here,
Refer Figure (e).
Write the formula for triangle.
Write the formula for rectangle.
Conclusion:
Refer Figure (e).
Calculate the area under the
Substitute
Substitute
Calculate the work done by the force
Substitute
Thus, the work done by the force on the block is
f)
The work of a spring force.
Answer to Problem 1PP
The work done by the force on the block is
Explanation of Solution
Given:
The stiffness of the spring is
The spring is originally compressed to
Draw the free body diagram of block as shown in Figure (f).
Write the formula for work done force
Here,
Conclusion:
Refer Figure (f).
Here, the block is subjected to spring force only.
When the spring is originally compressed to
When the spring is released, the displaced to
Substitute
Thus, the work done by the spring force on the block is
g)
The work of a force.
Answer to Problem 1PP
The work done by the force on the block is
Explanation of Solution
Given:
The force acting on the block is
The displacement of the block is
Draw the free body diagram of block as shown in Figure (g).
Write the formula for work done force
Here,
Conclusion:
Refer Figure (g).
Resolve the force along
Substitute
Thus, the work done by the force on the block is
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Chapter 14 Solutions
Engineering Mechanics: Dynamics (14th Edition)
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