Chapter 11: Q. 1 (page 286)
At what speed do a bicycle and its rider, with a combined mass of , have the same momentum as a car traveling at ?
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Chapter 11: Q. 1 (page 286)
At what speed do a bicycle and its rider, with a combined mass of , have the same momentum as a car traveling at ?
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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?
In FIGURE EX11.5, what value of gives an impulse of ?

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.
A tennis player swings her 1000 g racket with a speed of 10 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 20 m/s. The ball rebounds at 40 m/s.
a. How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision.
b. If the tennis ball and racket are in contact for 10 ms, what is the average force that the racket exerts on the ball? How does this compare to the gravitational force on the ball?
Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of 2.0 km and a mass ofhits the earth with an impact speed of .
a. What is the earth’s recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.)
b. What percentage is this of the earth’s speed around the sun? The earth orbits the sun at a distance of.
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