Centripetal Force Vertical Motion Circular Motion Lesson 4

Centripetal Force: Vertical Motion Circular Motion: Lesson 4

Vertical Centripetal Motion • When working in the vertical plane with centripetal motion we must now consider gravity. All problems that involve vertical centripetal motion now become a Net Force Problem. The force will vary depending on the direction of the force Consider the following: 1. A ball with a mass of 200 g is swung on the end of a string that is 40 cm long. The ball makes 5 revolutions in 2. 4 s. a. What is the period of rotation? b. What is the centripetal speed?

Note: • the speed depends only on radius; the mass of the object is irrelevant.

Remember the centripetal force is the net force (the vector sum of all forces acting on the object) c. What is the force of tension on the ball, at the top of the swing? the net force to keep it moving at the top of the loop will be less because gravity is helping to move the ball

d. What is the force of tension on the ball, at the bottom of the swing? The net force at the bottom of the loop will be greater because it must overcome gravity

• Example 2: A 2. 0 kg object is swung at the end of a 2. 0 m rope vertically. It completes one full revolution in 2. 0 s. What is the tension in the rope at the top and the bottom of its path?

Finding Minimum Speed • In order for an object to remain in circular motion we must find the minimum speed at the top of the motion so it does not fall. • In this case, the tension would be 0

• The cars on a rollercoaster have a mass of 1200 kg, and travel in a vertical loop-de-loop that has a radius of 30 m. What speed must the rollercoaster maintain to complete the loop? Solution Force centripetal must be greater than the force due to gravity.

Example 4: A 1000 kg truck with a speed of 16. 0 m/s travels over a hill. If the radius of the hill from the top position is 90. 0 m, what is the normal force acting at the top of the hill on the truck?

Homework: