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Chapter 11: Q. 61 (page 290)
A 500 g particle has velocity at . Force , where t is in s, is exerted on the particle between. This force increases from 0 N at and then back to . What is the particle’s velocity at t = 2 s?
The particle's velocity atis
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A cart is released from rest from the bottom of a frictionless, ramp. The cart rolls down the ramp and bounces off a rubber block at the bottom. FIGURE Pshows the force during the collision. After the cart bounces, how far does it roll back up the ramp?
A sled slides along a horizontal surface on which the coefficient of kinetic friction is . Its velocity at point is and at point is . Use the momentum principle to find how long the sled takes to travel from to.
Section 11.6 found an equation for vmax of a rocket fired in deep space. What is vmax for a rocket fired vertically from the surface of an airless planet with free-fall acceleration g? Referring to Section 11.6, you can write an equation for ∆Py, the change of momentum in the vertical direction, in terms of dm and dvy. ∆Py is no longer zero because now gravity delivers an impulse. Rewrite the momentum equation by including the impulse due to gravity during the time dt during which the mass changes by dm. Pay attention to signs! Your equation will have three differentials, but two are related through the fuel burn rate R. Use this relationship—again pay attention to signs; m is decreasing—to write your equation in terms of dm and dvy. Then integrate to find a modified expression for vmax at the instant all the fuel has been burned.
a. What is vmax for a vertical launch from an airless planet ? Your answer will be in terms of mR, the empty rocket mass; mF0, the initial fuel mass; vex, the exhaust speed; R, the fuel burn rate; and g.
b. A rocket with a total mass of 330,000 kg when fully loaded burns all 280,000 kg of fuel in 250 s. The engines generate 4.1 MN of thrust. What is this rocket’s speed at the instant all the fuel has been burned if it is launched in deep space ? If it is launched vertically from the earth?
A 1000 kg cart is rolling to the right at 5.0 m/s. A 70 kg man is standing on the right end of the cart. What is the speed of the cart if the man suddenly starts running to the left with a speed of 10 m/s relative to the cart?
In FIGURE P11.57, a block of mass m slides along a frictionless track with speed . It collides with a stationary block of mass M. Find an expression for the minimum value of that will allow the second block to circle the loop-the-loop without falling off if the collision is (a) perfectly inelastic or (b) perfectly elastic.
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