Physics Principles with Applications1912 solutions
Consider as a system the Sun with the Earth in a circular orbit around it. Find the magnitude of the change in the velocity of the Sun relative to the center of mass of the system over a six-month period. Ignore the influence of other celestial objects. You may obtain the necessary astronomical data from the endpapers of the book.
There are (one can say) three coequal theories of motion for a single particle: Newton’s second law, stating that the total force on the particle causes its acceleration; the work–kinetic energy theorem, stating that the total work on the particle causes its change in kinetic energy; and the impulse–momentum theorem, stating that the total impulse on the particle causes its change in momentum. In this problem, you compare predictions of the three theories in one particular case. A 3.00-kg object has velocity 7.00 jm/s. Then, a constant net force 12i^Nacts on the object for 5.00 s. (a) Calculate the object’s final velocity, using the impulse–momentum theorem. (b) Calculate its acceleration from a→=v→f-v→i/Δt . (c) Calculate its acceleration from aa→=∑F→/Δt. (d) Find the object’s vector displacement from Δr→=v→it+12a→t2. (e) Find the work done on the object from W=F→·Δr→. (f) Find the final kinetic energy from 12mvf2=12mv→f·v→f. (g) Find the final kinetic energy from 12mvi2+W(h) State the result of comparing the answers to parts (b) and (c), and the answers to parts (f) and (g).
A 2.00-g particle moving at 8.00 m/s makes a perfectly elastic head-on collision with a resting 1.00-g object. (a) Find the speed of each particle after the collision. (b) Find the speed of each particle after the collision if the stationary particle has a mass of 10.0 g. (c) Find the final kinetic energy of the incident 2.00-g particle in the situations described in parts (a) and (b). In which case does the incident particle lose more kinetic energy?
In the 1968 Olympic games, University of Oregon jumper Dick Fosbury introduced a new technique of high jumping called the “Fosbury flop.” It contributed to raising the world record by about 30 cm and is currently used by nearly every world-class jumper. In this technique, the jumper goes over the bar face-up while arching her back as much as possible as shown in Figure P9.92a. This action places her center of mass outside her body, below her back. As her body goes over the bar, her center of mass passes below the bar. Because a given energy input implies a certain elevation for her center of mass, the action of arching her back means that her body is higher than if her back were straight. As a model, consider the jumper as a thin uniform rod of length L. When the rod is straight, its center of mass is at its center. Now bend the rod in a circular arc so that it subtends an angle of 900 at the center of the arc as shown in Figure P9.92b. In this configuration, how far outside the rod is the center of mass?
Two particles with masses m and 3m are moving toward each other along the x axis with the same initial speeds vi . Particle m is traveling to the left, and particle 3m is traveling to the right. They undergo an elastic glancing collision such that particle m is moving in the negative y direction after the collision at a right angle from its initial direction. (a) Find the final speeds of the two particles in terms of vi . (b) What is the angle θ at which the particle 3m is scattered?
Sand from a stationary hopper falls onto a moving conveyor belt at the rate of 5.00 kg/s as shown in Figure P9.94. The conveyor belt is supported by frictionless rollers and moves at a constant speed of v = 0.750 m/s under the action of a constant horizontal external force F→extsupplied by the motor that drives the belt. Find (a) the sand’s rate of change of momentum in the horizontal direction, (b) the force of friction exerted by the belt on the sand, (c) the external force F→ext, (d) the work done by F→ext in 1 s, and (e) the kinetic energy acquired by the falling sand each second due to the change in its horizontal motion. (f) Why are the answers to parts (d) and (e) different?
Question:A12.0-g wad of sticky clay is hurled horizontally at a 100-g wooden block initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides before 7.50 m coming to rest. If the coefficient of friction between the block and the surface is 0.650, what was the speed of the clay immediately before impact?
Question:A wad of sticky clay of mass m is hurled horizontally at a wooden block of mass M initially at rest on a horizontal surface. The clay sticks to the block. After impact, the block slides a distance d before coming to rest. If the coefficient of friction between the block and the surface isμ, what was the speed of the clay immediately before impact?
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