Cite two examples in which a force is exerted on an object without doing any work on the object.
Two examples where the exerted force does no work are
1. A person carrying a suitcase on his head and walks, and
2. A person is revolving a piece of stone tied to a rope around himself at constant speed.
There is no work done when the force exerted is perpendicular to the displacement.
When a person carries a suitcase on his head and moves from one point to another, no work is done. This is because the force exerted on the suitcase is upward which balances the gravitational force on the suitcase. The displacement is horizontal. Thus the force is perpendicular to the displacement and no work is done.
When a person is revolving a piece of stone tied to a rope with constant speed around himself, no work is done. This is because the force applied by the person on the rope and the stone is radially inward which balances the centripetal force, whereas the displacement is tangential. Thus the force is perpendicular to the displacement and no work is done.
In Chapter 7, the work–kinetic energy theorem, W=DK, was introduced. This equation states that work done on a system appears as a change in kinetic energy. It is a special-case equation, valid if there are no changes in any other type of energy such as potential or internal. Give two or three examples in which work is done on a system but the change in energy of the system is not a change in kinetic energy.
A daredevil plans to bungee jump from a balloon 65.0 m above the ground. He will use a uniform elastic cord, tied to a harness around his body, to stop his fall at a point 10.0 m above the ground. Model his body as a particle and the cord as having negligible mass and obeying Hooke’s law. In a preliminary test he finds that when hanging at rest from a 5.00-m length of the cord, his body weight stretches it by 1.50 m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon. (a) What length of cord should he use? (b) What maximum acceleration will he experience?
A child of mass m starts from rest and slides without friction from a height h along a slide next to a pool (Fig. P8.27). She is launched from a height h/5 into the air over the pool. We wish to find the maximum height she reaches above the water in her projectile motion. (a) Is the child–Earth system isolated or
Non-isolated? Why? (b) Is there a non-conservative force acting within the system? (c) Define the configuration of the system when the child is at the water level as having zero gravitational potential energy. Express the total energy of the system when the child is at the top of the waterslide. (d) Express the total energy of the system when the child is at the launching point. (e) Express the total energy of the system when the child is at the highest point in her projectile motion. (f) From parts (c) and (d), determine her initial speed at the launch point in terms of g and h. (g) From parts (d), (e), and (f), determine her maximum airborne height in terms of h and the launch angle. (h) Would your answers be the same if the waterslide were not frictionless? Explain.
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