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**Group Problem #4 Physics 111-4 Spring 2012 Page 1 of 1**

Homework #4

**Chapter 9: Systems of Particles **

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#2: Explain why a high-jumper’s center of mass need not clear the bar.

#6: Why are cars designed so that their front ends crumple during an accident?

#11: Two identical satellites are going in opposite directions in the same circular orbit when they collide head-on. Describe their subsequent motion if the collision is (a) elastic or (b) inelastic.

#12: A 28kg child sits at one end of a 3.5m long seesaw. Where should her 65kg father sit so the center of mass will be at the center of the seesaw?

#15: Three identical masses lie at the corners of an equilateral triangle of side L. Find the center of mass.

#18: A 60kg skater, at rest on frictionless ice, tosses a 12kg snowball with velocity 𝑣⃗ = 53.0𝑖̂ +

14.0𝑗̂ 𝑚/𝑠 , where the x- and y- axes are in the horizontal plane. Find the skater’s subsequent velocity.

#21: A 150g trick baseball is thrown at 65 km/hr. It explodes in flight into two pieces, with a

38kg piece continuing straight ahead at 8.5km/hr. How much energy do the pieces gain in the explosion?

#24: High-speed photos of a 220µg flea jumping vertically show that the jump lasts 1.2ms and involves an average vertical acceleration of 100g. What (a) average force and (b) impulse does the ground exert on the flea during its jump? (c) What’s the change in the flea’s momentum during the jump?

#29: Two identical trucks have mass 5500 kg when empty and the maximum permissible load for each is 8000kg. The first truck, carrying 3800kg, is at rest. The second truck plows into it at 65 km/hr and the pair moves away at 40 km/hr. As an expert witness, you’re asked to determine whether the first truck was overloaded. What do you report?

#31: Playing in the street, a child accidentally tosses a ball at 18m/s toward the front of a car moving toward him at 14 m/s. What’s the ball’s speed after it rebounds elastically from the car?

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#36: Wildlife biologists fire 20g rubber bullets to stop a rhinoceros from charging at 0.81 m/s.

The bullets strike the rhino and drop vertically to the ground. The biologist’s gun fires 15 bullets each second, at 73 m/s and it takes 34s to stop the rhino. (a) What impulse does each bullet deliver? (b)

What’s the rhino’s mass? Neglect forces between the rhino and the ground.

#42: A firecracker, initially at rest, explodes into two fragments. The first, of mass 14g, moves in the +x direction at 48 m/s. The second moves at 32 m/s. Find the second fragment’s mass and the direction of motion.

#51: A 60kg astronaut floating in space simultaneously tosses away a 14kg oxygen tank and a

5.8kg camera. The tans moves in the x-direction at 1.6m/s and the astronaut recoils at 0.85 m/s in a direction 200° counterclockwise from the x-axis. Find the camera’s velocity.

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#58: You’re an accident investigator at a scene where a drunk driver in a 16kg car has plowed into a 1300kg parked car with its brake set. You measure the skid marks showing that the combined wreckage moved 25m before stopping, and you determine a frictional coefficient of 0.77. What do you report for the drunk driver’s speed just before the collision?

#63: A 1200-kg Toyota and a 2200kg Buick collide at right angles at an intersection. They skid together 22m; the coefficient of friction is 0.91. Show that at least one car must have exceeded the 25 km/hr speed limit at the intersection.