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Chapter 7: Q80P (page 176)
Numerical integration. A breadbox is made to move along an x axis from by a force with a magnitude given by , with x in meters and F in Newton. (Here exp is the exponential function.) How much work is done on the breadbox by the force?
Work done by the force F on the breadbox is .
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In Fig.7-47 , a cord runs around two massless, frictionless pulleys. A canister with mass m 20 kg hangs from one pulley, and you exert a force on the free end of the cord. (a) What must be the magnitude of if you are to lift the canister at a constant speed? (b) To lift the canister by 2.0 cm , how far must you pull the free end of the cord? During that lift, what is the work done on the canister by (c) your force (via the cord) and (d) the gravitational force? (Hint: When a cord loops around a pulley as shown, it pulls on the pulley with a net force that is twice the tension in the cord.)
As a particle moves along an x axis, a force in the positive direction of the axis acts on it. Figure 7-50shows the magnitude Fof the force versus position x of the particle. The curve is given by , with . Find the work done on the particle by the force as the particle moves fromto by (a) estimating the work from the graph and (b) integrating the force function.
In the block鈥搒pring arrangement of Fig., the block鈥檚 mass is and the spring constant is. The block is released from position. What is (a) the block鈥檚 speed at, (b) the work done by the spring when the block reaches, (c) the instantaneous power due to the spring at the release point , (d) the instantaneous power at, and (e) the block鈥檚 position when the power is maximum?
(a) at a certain instant, a particle-like object is acted on by a force while the object鈥檚 velocity is . What is the instantaneous rate at which the force does work on the object? (b) At some other time, the velocity consists of only a y component. If the force is unchanged and the instantaneous power is -12 W , what is the velocity of the object?
A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force along an x axis is applied to the block. The force is given by , where x is in meters and the initial position of the block is x=0. (a) What is the kinetic energy of the block as it passes through x=2.0 m? (b) What is the maximum kinetic energy of the block between x=0 and x=2.0 m?
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