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# 7 Problems in Mechanics: Force and motion, work power energy

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Question 1: A 3.0-g bullet traveling at 350 m/s hits a tree and slows down uniformly to a stop while penetrating a distance of 12 cm into the tree's trunk. What was the force exerted on the bullet in bringing it to rest?

Question 2: A big car of mass 2m travels at speed v, and a small car of mass m travels with a speed 2v. Both skid to a stop with the same coefficient of friction.
(a) The small car will have:
(1) a longer stopping distance
(2) the same stopping distance
(3) a shorter stopping distance

(b) Calculate the ratio of the stopping distance of the small car to that of the large car. (Use the work-energy theorem, not Newton's laws.)

Question 3: A student has six textbooks, each 4.0 cm thick and 30 N in weight. What is the minimum work the student would have to do to place all the books in a vertical stack, starting with all the books on the surface of the table?

Question 4:
Under what conditions would kinetic energy not be conserved? Explain each response and back up your response using principles of physics.

Question 5: A skier coasts down a very smooth, 10-m-high slope. If the speed of the skier on the top of the slope is 5.0 m/s, what is his speed at the bottom of the slope?

Question 6: A 1.5-kg box that is sliding on a frictionless surface with a speed of 12 m/s approaches a horizontal spring. The spring has a spring constant of 2000 N/m. (a) How far will the spring be compressed in stopping the box? (b) How far will the spring be compressed when the box's speed is reduced to half of its initial speed?

Question 7: A 3250-kg aircraft takes 12.5 min to achieve its cruising altitude of 10.0 km and cruising speed of 850 km/h. If the plane's engines deliver, on average, 1500 hp of power during this time, what is the efficiency of the engines (neglecting air resistance)?

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