Calculate the work performed by a person who exerts a force of 30 N(N = newtons) to move a box 30 meters if the force were (a) exactly parallel to the direction of movement, and (b)45° to the direction of movement. Do the relative magnitudes make sense?
(a)
Interpretation
To calculate the work performed by a person who exerts a force of 30N to move a box 30 meters if the force were exactly parallel to the direction of movement.
Concept introduction
The work is performed on an object when an object moves a certain distance s due to the force F. Mathematically, it is indicated by the dot product of the force vector F and the distance vector s. The mathematical equation is given below,
Work = F.s = |F||s| cos Ѳ
Where Ѳ is the angle between the vectors F and s. The unit of work is joules. Work is a way to transfer the energy. The energy is defined as the ability to do work and so energy and work are described using the same unit in joules.
Answer to Problem 2.1E
Work exactly parallel to the direction of movement = 900 J
Explanation of Solution
The work is defined as force x displacement [distance].
In the given question
work = 30N
distance = 30m
Work = F.s
Therefore work = 30 N.30 m= 900 J
Thus the Work exactly parallel to the direction of movement = 900 J
(b)
Interpretation
To calculate the work performed by a person who exerts a force of 30N to move a box 30 meters if the force were 45° to the direction of movement.
Concept introduction
The work is performed on an object when an object moves a certain distance s due to the force F. Mathematically, it is indicated by the dot product of the force vector F and the distance vector s. The mathematical equation is given below,
Work = F.s = |F||s| cos Ѳ
Where Ѳ is the angle between the vectors F and s. The unit of work is joules. Work is a way to transfer the energy. The energy is defined as the ability to do work and so energy and work are described using the same unit in joules.
Answer to Problem 2.1E
Work were 45° to the direction of movement = 640 J
Explanation of Solution
The work is defined as force x displacement [distance].
In the given question
work = 30N
degree = 45°
Work = F.s = |F||s| cos Ѳ
Therefore work = 30 N. 30m cos 45°
= 30 x 30 x0.71
Work = 640 J
Thus the work at 45° to the direction of movement = 640 J
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