## Phys 211 College Physics I

Problem Session 1

1. An empty 15,000 kg coal car is coasting at a speed on a level track at 5.00 m/s. Suddenly 5000 kg of coal is dumped into it from directly above it. The coal initially has zero horizontal velocity. Find the speed of the car.   Ans: 3.75 m/s

2. A 1200 kg gun mounted on wheels shoots an 8.00 kg projectile with a muzzle velocity of 600 m/s at an angle of 30.0o above the horizontal. Find the horizontal recoil speed of the gun.   Ans: 3.46 m/s

3. A ball of mass m at rest at the coordinate origin explodes into three equal pieces. At a certain instant, one piece is on the x axis at x = 40 cm and another is at x = 20 cm, y = -60 cm. Where is the third piece at that instant?   Ans: x = -60 cm, y = 60 cm

4. A flywheel turns a 480 rpm. Compute the angular speed at any point on the wheel and the tangential speed 30.0 cm from the center.   Ans:50.3 rad/s, 15.1 m/s

5. Through how many radians does a point on the earth's surface move in 6.00 h as a result of the earth's rotation? What is the speed of a point on the equator? Take the radius of the earth to be 6370 km.   Ans: 1.57 rad, 463 m/s

6. (a) Compute the radial acceleration of a point at the equator of the earth. (b) Repeat for the north pole of the earth.   Ans: 0.0337 m/s2, zero

7. A car has wheels of radius 30 cm. It starts from rest and accelerates uniformly to a speed of 15 m/s in a time of 8.0 s. Find the angular acceleration of its wheels and the number of rotations one wheel makes in this time.   Ans: 6.3 rad/s2, 32 rev

8. A pendulum 80.0 cm long is pulled to the side, so that its bob is raised 20.0 cm from its lowest position, and is then released. As the 50.0 g bob moves through its lowest position, (a) what is its speed and (b) what is the tension in the pendulum cord?   Ans: (a) 1.98 m/s, (b) 0.735 N

9. A roller coaster is just barely moving as it goes over the top of a hill. It rolls nearly without friction down the hill and then up over a lower hill that has a radius of curvarure of 15 m. How much higher must the first hill be than the second if the passengers are to exert no force on the seat as they pass over the top of the lower hill?   Ans: 7.5 m

10. A belt passes over a wheel of radius 25 cm. If a point on the belt has a speed of 5.0 m/s, How fast is the wheel turning?   Ans: 20 rad/s

11. A 2.0 kg block of wood rests on a long tabletop. A 5.0 g bullet moving horizontally with a speed of 150 m/s is shot into the block and sticks in it. The block then slides 270 cm along the table and stops. (a) Find the speed of the block just after impact. (b) Find the friction force between block and table.   Ans: (a) 0.38 m/s, (b) 0.52 N