Vertical Circular Motion
1) The maximum tension that a 0.5 m string can tolerate is 14 N. A 0.25 kg ball attached to this string is being whirled in a vertical circle. What is the maximum speed that the ball can have (a) at the top of the circle and (b) at the bottom of the circle?
2) A 2100 kg demolition ball swings at the end of a 15 m cable on the arc of a vertical circle. At the lowest point of the swing, the ball is moving at a speed of 7.6 m/s. Determine the tension in the cable.
3) A motorcycle has a constant speed of 25 m/s as it passes over the top of a hill whose radius of curvature is 126 m. The mass of the motorcycle and driver is 342 kg. Find the magnitude of (a) the net centripetal force and (b) the normal force that acts on the bike.
4) In a trapeze act, a man, hanging upside down, holds onto his partner who weighs 475 N. How much force must the man exert if they are moving at 4 m/s at the bottom of a circular arc of radius 6.5 m?
5) A downhill skier whose mass is 50 kg, attains a speed of 21 m/s just as she reaches the point where a jump is necessary (at the bottom of a vertical circle of radius 27 m). Determine the normal force acting on the skis at that point.
6) A rollercoaster at an amusement park has a dip that bottoms out in a vertical circle of radius 20 m. Passengers feel the seat of the car pushing on them with a force equal to twice their weight as they go through the dip. How fast is the rollercoaster moving at that point?
7) Passengers in a plane can feel weightless if the plane flies over the top of a vertical circle. At a speed of 215 m/s, what is the radius of the vertical circle that the pilot must use for this to happen? (Hint: if the passengers feel weightless, what is the normal force acting on them? Note: This is how the space scenes in the movie “Apollo 13” were filmed.)
8) A motorcycle is traveling up one side of a hill and down the other side. The crest is a circular arc with a radius of 45 m. (a) Determine the maximum speed that the cycle can have while moving over the crest without losing contact with the road. (b) Which critical speed is this (minimum or maximum)?
Vertical Circular Motion
1) The maximum tension that a 0.5 m string can tolerate is 14 N. A 0.25 kg ball attached to this string is being whirled in a vertical circle. What is the maximum speed that the ball can have (a) at the top of the circle and (b) at the bottom of the circle?
2) A 2100 kg demolition ball swings at the end of a 15 m cable on the arc of a vertical circle. At the lowest point of the swing, the ball is moving at a speed of 7.6 m/s. Determine the tension in the cable.
3) A motorcycle has a constant speed of 25 m/s as it passes over the top of a hill whose radius of curvature is 126 m. The mass of the motorcycle and driver is 342 kg. Find the magnitude of (a) the net centripetal force and (b) the normal force that acts on the bike.
4) In a trapeze act, a man, hanging upside down, holds onto his partner who weighs 475 N. How much force must the man exert if they are moving at 4 m/s at the bottom of a circular arc of radius 6.5 m?
5) A downhill skier whose mass is 50 kg, attains a speed of 21 m/s just as she reaches the point where a jump is necessary (at the bottom of a vertical circle of radius 27 m). Determine the normal force acting on the skis at that point.
6) A rollercoaster at an amusement park has a dip that bottoms out in a vertical circle of radius 20 m. Passengers feel the seat of the car pushing on them with a force equal to twice their weight as they go through the dip. How fast is the rollercoaster moving at that point?
7) Passengers in a plane can feel weightless if the plane flies over the top of a vertical circle. At a speed of 215 m/s, what is the radius of the vertical circle that the pilot must use for this to happen? (Hint: if the passengers feel weightless, what is the normal force acting on them? Note: This is how the space scenes in the movie “Apollo 13” were filmed.)
8) A motorcycle is traveling up one side of a hill and down the other side. The crest is a circular arc with a radius of 45 m. (a) Determine the maximum speed that the cycle can have while moving over the crest without losing contact with the road. (b) Which critical speed is this (minimum or maximum)?