AP Physics Daily Problem #31

Transcription

1 AP Physics Daily Problem #31 A 10kg mass is whirled around on the end of a 3m long cord. The speed of the mass is 7m/s. Ignore gravitational forces. 3.0m 7.0m/s Draw a free body diagram of the mass. (hint: draw it as if the rotation circle is viewed edge-on) Determine the acceleration of the mass What is the tension in the cord?

2 AP Physics Daily Problem #32 A 10kg mass is whirled around on the end of a cord (fixed to the ceiling) in a horizontal circle of 3.0m radius. The speed of the mass is 6.0m/s. 3.0m radius 6.0m/s Draw a free body diagram of the mass. Show the horizontal and vertical components of the tension force. (hint: this is the most important step in the solution. Do it carefully!) Determine the acceleration of the mass Determine the horizontal component of the tension force Determine the vertical component of the tension force Determine the angle (measured from the vertical) of the cord. What is the tension in the cord?

3 AP Physics Daily Problem #33 The Spinout ride at Magic Mountain consists of a large vertical rotating drum. It has a radius of 5 meters and rotates at 20RPM. The rider is on the inside of the drum and is accelerated toward the center of the drum by the wall. The floor drops away, leaving the rider pinned to the wall. 5.0m radius 20.0 RPM Draw a free body diagram of the rider. Show all forces. (hint: Use a frame of reference with the rider moving away from the observer) Determine the acceleration of the rider Determine the centripetal force on a 50.0kg rider. Determine the minimum coefficient of friction to allow the rider to stay on the wall without sliding when the floor drops away.

4 AP Physics Daily Problem #34 (1967 #9) Two objects of equal mass on a smooth horizontal table top are connected by string A and B to a fixed point O as shown in the diagram. The system consisting of the two objects and the two strings rotates in a horizontal plane at constant angular velocity ω about O. Show that the ratio of the tension in string B to the tension in string A is 2/3. D D O A B

5 AP Physics Daily Problem #35 (1969 #7) A boy stands in a room and swings a small block on a string so that the path of the block is a circle with a radius of 1 meter and the string is in a vertical plane. The mass of the block is 0.4kg and at the top of the path the tension in the string is 6N. (a) In the reference frame of the room, describe the forces acting upon the block at the instant that it passes the top of its path. (neglect air friction) (b) path. Determine the value of the centripetal acceleration of the block at the top of its

6 AP Physics Daily Problem #36 Read Chapter 6 (Hecht or Giancoli) before doing this problem! A man carries a 50kg backpack up a flight of stairs. Each step is 10.0cm high and the man climbs 150 steps. He then walks 100m on a horizontal surface. (a) How much work did the man do on the backpack while climbing the steps? (b) How much work did the man do on the backpack while walking on the horizontal surface? (c) The man then drops the backpack from a balcony. It falls to the the level of the bottom of the stairs. How fast is the backpack going when it reaches its original level? Neglect friction, and use only energy methods (not kinematics!) to solve this problem.

7 AP Physics Daily Problem #37 A 1.0kg ball is thrown upward with an initial velocity of 20m/s. Answer the following using only energy methods: How much kinetic energy does the ball have when it is thrown? How high does the ball go? How fast is the ball going when it is 12.0m above the starting point?

8 AP Physics Daily Problem #38 The Earth has a mass of 5.97E24kg, and the Sun has a mass of 1.99E30kg. They are a distance of 149.6E6km apart Determine the attractive force between the Earth and the Sun. What is the earth s acceleration toward the sun? Using only the information above, determine the earth s velocity in its orbit.

9 AP Physics Daily Problem #39 Planet X has a mass of 2.5x10 24 kg, and the star it orbits (in a circular orbit) has a mass of 8.5x10 29 kg. They are a distance of 80.0x10 6 km apart Determine the gravitational force between Planet X and its star. Determine the speed of planet X in its orbit. Determine the orbital period of Planet X in days. Consider a second planet, Planet Y, which has twice the mass of Planet X, but is the same orbit. What is the ratio of Planet Y s orbital velocity to that of Planet X. Justify your answer on the back of this sheet.

10 AP Physics Daily Problem #40 The Moon has a mass of 7.35x10 22 kg and a radius of 1740km. Determine the gravitational acceleration at the surface of the moon. The lunar amusement park has a roller coaster whose cars have a maximum speed of 25m/s. What is the maximum size of a loop in this roller coaster if the riders are to not experience negative G s?