Concept explainers
A helicopter rescues a trapped person of mass m = 65.0 kg from a flooded river by lifting the person vertically upward using a winch and rope. The person is pulled 12.0 m into the helicopter with a constant force that is 15% greater than the person’s weight. a. Find the work done by each of the forces acting on the person. b. Assuming the survivor starts from rest, determine his speed upon reaching the helicopter.
(a)
The work done by each of the forces acting on the person.
Answer to Problem 10PQ
The work done by gravitational force on the person is
Explanation of Solution
In this problem, there are two forces acting on the person which are the gravitational force of attraction or weight acting downward and tension in the rope acting upward.
Write the expression for the weight of the person.
Here,
It is given that tension is
Write the expression for the tension in the rope.
Here,
Helicopter is lifting the person vertically upward. The gravitational force on person is antiparallel to displacement of the person. The tension is parallel to displacement of the person. This implies that work done by gravitational force is negative and that by tension is positive.
Write the expression for the work done by a force.
Here,
Using equation (III),write the expression for the work done by gravitational force on person.
Here.
Using equation (III),write the expression for the work done by tension in rope on person.
Here.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the work done by gravitational force on the person is
(b)
The speed of survivor upon reaching the helicopter assuming he starts from rest.
Answer to Problem 10PQ
The speed of survivor upon reaching the helicopter assuming he starts from rest is
Explanation of Solution
Write the equation for the change in kinetic energy of the person using work energy theorem.
Here,
Write the expression for the total work done.
Here,
Write the expression for change in kinetic energy.
Here,
Substitute equation (VIII) and (VII) in equation (VI) to expand the equation.
Substitute
Conclusion:
Substitute
Therefore, The speed of survivor upon reaching the helicopter assuming he starts from rest is
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Chapter 9 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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