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Chapter 9: Q. 23 (page 228)
A particle moving on the axis experiences a force given by , where is a constant. How much work is done on the particle as it moves from to ?
Work done by particle
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An kg crate is pulled m up a incline by a rope angled above the incline. The tension in the rope is N, and the crate鈥檚 coefficient of kinetic friction on the incline is .
a. How much work is done by tension, by gravity, and by the normal force?
b. What is the increase in thermal energy of the crate and incline?
The gravitational attraction between two objects with masses and , separated by distance x, is , where G is the gravitational constant.
a. How much work is done by gravity when the separation changes from to ? Assume .
b. If one mass is much greater than the other, the larger mass stays essentially at rest while the smaller mass moves toward it. Suppose a comet is passing the orbit of Mars, heading straight for the sun at a speed of What will its speed be when it crosses the orbit of Mercury? Astronomical data are given in the tables at the back of the book, and .
A hydroelectric power plant uses spinning turbines to transform the kinetic energy of moving water into electric energy with efficiency. That is, of the kinetic energy becomes electric energy. A small hydroelectric plant at the base of a dam generates of electric power when the falling water has a speed of . What is the water flow rate鈥攌ilograms of water per second鈥攖hrough the turbines?
A gardener pushes a lawnmower whose handle is tilted up above horizontal. The lawnmower鈥檚 coefficient of rolling friction is . How much power does the gardener have to supply to push the lawnmower at a constant speed of ? Assume his push is parallel to the handle.
a. Starting from rest, a crate of mass is pushed up a frictionless slope of angle by a horizontal force of magnitude . Use work and energy to find an expression for the crate鈥檚 speed when it is at height above the bottom of the slope.
b. Doug uses a N horizontal force to push a kg crate up a -m-high, frictionless slope. What is the speed of the crate at the top of the slope?
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