Radial Net Forces and Circular Motion

Name Central Net Force Model Worksheet 1: Radial Net Forces and Circular Motion 1. A bowling ball rolls down the hallway. a. To curve the ball turn in a smooth circular turn to the right, draw a picture to indicate how you would push on the ball to make it turn. One needs to push the ball toward the center of the circle you want the ball to move in. b. While you are curving the ball's path, are the forces on the ball balanced? Draw a force diagram for the ball. The forces on the ball are not balanced. If they were the ball would go in a straight line. The force diagram to the right is from the point of view of someone watching the ball come at them. FN = Fnet FN = Fg c. Is the ball accelerating? If so, what is changing about the velocity? Assuming the ball is not changing speed, it is accelerating because the direction of the ball's motion is changing. 2. An airplane banks and makes a wide circle. Fair a. Draw a force diagram for a head-on view of the banking plane. b. Name the force that allows the plane to travel in a circle. The horizontal component of the force of the air on the wings. Fg 3. A car enters a circular turn at a constant speed. a. Name the force (the interaction between objects) that allows the car to travel in a circle. In what direction does this force push on the car? Draw a force diagram for FN the car as it approaches head-on. Fnet The interaction that allows the car to travel in a circle is the = surface of the road acting on the tires. If the car is not sliding we call this interaction static friction. This force is = always acting toward the center of the circle the car is Fg making. At the moment in the force diagram the force is acting to the right. b. Describe the motion of the car if the force you described in part "a" suddenly vanished. The car would travel in a straight line toward you! It would move at constant speed along the tangent to the circle. c. If the 35 meter radius turn is level, the car has a mass of 1200 kg, and the coefficient of friction between the tires and the road is .85, what is the maximum speed that a car can travel through the turn without the tires slipping? Fnet =F fs = Fs N = smg 2 mv gr  v= s mg = s r N v = .85(10 kg )35 m 17 = sm 4. The international space station orbits earth once every 90 minutes. a. Name the force that allows the ISS to orbit earth. Draw a force Diagram of the ISS. The force of gravity of the earth on the space station. b. Explain why the space station doesn't crash to earth due to the force on it. Because the space station keeps moving forward as the earth pulls it inward. This causes the space station to keep falling around the earth. c. The ISS 420,000 kg and orbits 408,000 meters above the Earth. The Earth has a radius of 6,371,000 meters. What is the tangential velocity of the ISS as it orbits every 90 minutes? 𝑣= 2𝜋𝑟 𝑇 = 2𝜋(6,371,000𝑚+408,000𝑚) 90 𝑚𝑖𝑛∗60𝑠𝑒𝑐/𝑚𝑖𝑛 = 7,888𝑚/𝑠 Be sure to add Earth radius plus height for the radius of the circle in the calculation. Ffs d. Calculate the centripetal acceleration of and the net force on the ISS as it orbits. 𝑎𝑐 = 𝑣2 𝑟 𝐹 = 𝑚𝑎 = (7888)2 = (6,371,000𝑚+408,000𝑚) 𝑚 (420,000𝑘𝑔) (9.18 ) 𝑠2 = 9.18 𝑚 𝑠2 = 3,856, 000 𝑁 5. a. Draw a force diagram (side view) for a rollercoaster on level track. Should the forces perpendicular to the track be balanced? If the forces are unbalanced, explain why there is a net force and the direction of the net force. FN The forces perpendicular to each car are balanced. Fg b. Draw a force diagram (side view) for a rollercoaster traveling over the top of a hill. Should the forces perpendicular to the track be balanced? If the forces are unbalanced, explain why there is a net force and the direction of the net force. The forces perpendicular to each car are not balanced. The track has a curved path. The center of curvature of the track is below the car, therefore the car is accelerating downward. The circle shown (sometimes known as the kissing circle) has its center below the car. To be accelerating downward, the downward force of gravity must be larger than the upward normal force of the track. FN Fnet Fg c. Draw a force diagram (side view) for a rollercoaster traveling through a valley. Should the forces perpendicular to the track be balanced? If the forces are unbalanced, explain why there is a net force and the direction of the net force. The forces perpendicular to each car are not balanced. The track has a curved path. The center of curvature of the track is above the car, therefore the car is accelerating upward. The kissing circle shown in this case has its center above the car. To be accelerating upward, the upward force of the track on the car must be larger than the downward force of gravity on the car. FN Fg Fnet 6. Note the radial acceleration of the sphere is the centripetal acceleration. (c) Lastly calculate the velocity of the bob.