Problem 1. A 2000 kg car drives with constant speed around a 200-m-radius circular track with constant speed 50 mph. Find an acceleration of the car.

Problem 2. A car drives with constant speed around a flat 100-m-radius circular track. Coefficient of static friction between the tires of the car and the surface of the track is 0.2. Find the maximum speed of the car so that the car will stay on the track.

 

Problem 3. A 2 kg block on a 1-m-long rope swings in a circle on a horizontal frictionless surface. Find the speed of the block if the tension in the rope is 40 N.

 

Problem 4. A 1 kg ball swings in a vertical circle at the end of a 2 m long rope. The speed of the ball at the bottom of the circle is 2m/s. Find the tension in the rope at this point.

 

Problem 5. A 200 g ball swings in a vertical circle at the end of a 2 m long rope. The tension in the rope at the top of the circle is 5 N. Find the speed of the ball at this point.

 

Problem 6. A ball of mass 2 kg swings in a vertical circle on a 1-m-long rope. When the rope makes with horizontal the speed of the ball is 5 m/s. Find the tension of the rope at this point.

 

Problem 7. A ball of mass 5 kg swings in a vertical circle on a 2-m-long rope. When the rope makes , the tension in the rope is 30 N. Find the speed of the ball at this point. Find the magnitude of acceleration at this point.

 

Problem 8. A car drives over the top of the hill. The maximum speed the car can have without flying off the road is 30 m/s. Find the radius of the hill.

 

Problem 9. A ball swings in a vertical circle on a 50-cm-long rope. Find the minimum speed the ball should have at the top of the circle so that the rope does not go slack.

 

Problem 10. A disk of radius 20 cm is rotating in horizontal plane around the vertical axis through the center of the disk. The angular speed of the disk is 10 rad/s. A small block is attached to the disk at distance 15 cm from the center of the disk. Find an acceleration of the block.

 

Problem 11. A disk of radius 30 cm is rotating in horizontal plane around the vertical axis through the center of the disk. A small block is standing on the surface of the disk at distance 20 cm from the center of the disk. The coefficient of static friction between the surface of the disk and the block is 0.4. Find the maximum angular speed of the disk so that the block does not slip of the disk.

 

Problem 12. A ball is attached to a rope. The other end of the rope is attached to a ceiling. The ball is rotating in a horizontal circle as shown in the figure. The circle is 50 cm below the ceiling. Find the angular speed of the ball.