Physics SI Center of Mass Uniform Circular Motion

Physics SI Center of Mass Uniform Circular Motion

Quiz Review: �The questions was asking why the car was going off the road and could not follow the curve �The force between ____ and the tires was not great enough

Answer: Friction �Centripetal force is what stops the car from going straight �On an unbanked curve, friction between the tires and road keeps the car from flying off in a straight line �Example of not enough friction: Snow or hydroplaning, why it is so hard to turn

Equations for the Day: �X of center of mass = m 1 x 1 + m 2 x 2 …… / m 1 + m 2 …. �Can use for the Y direction also �V of center of mass = m 1 v 1 +m 1 v 1 … / m 1 + m 2 … �V of center of mass for circular motion = 2 пr / T �T = time to go around once �Ac = delta V / Delta t �Ac = V^2 / r �Fc = m Ac = m ( V^2 / r)

Practice Problem: �A 59 -kg woman and a 71 -kg man sit on a seesaw, 3. 5 m long. Where is their center of mass?

Solution: Xcm = 1. 95 m �I said the women was at (0, 0) �Mass women = 59 �X women = 0 �Mass man= 73 �X man = 3. 5 �X cm = (59)(0) + (73)(3. 5) / (59 +73) �= 1. 94 meters

Practice Problem 2: �A fisherman in a boat catches a great white shark with a harpoon. The shark struggles for a while and then becomes limp when at a distance of 300 m from the boat. The fisherman pulls the shark by the rope attached to the harpoon. During this operation, the boat (initially at rest) moves 45 m in the direction of the shark. The mass of the boat is 5400 kg. What is the mass of the shark? Pretend that the water exerts no friction.

Solution: 953 kg �X boat = -45 meters �X shark = 255 meters �M boat = 5400 �M shark = ? ? ? �Use x cm = xm +xm / m+m �Say center of mass is our location at the origin �So 0= xm +xm / m+m � 0 = 255(m) + (-45)(5400) / (5400 * m) � 0 = = 255(m) + (-45)(5400) � M = 45(5400) / 255 = 953 kg

Practice Problem 3: �A 5 kg ball is attached to a string and it rotated are with a radius of 8 m. If the ball revolves are 4 times in 2 seconds, what is the tension in the string? � ( I made this up, this is not realistic)

Solution: �Fc = m ac = m ( v^2 / r ) �Don’t know the velocity �Can us v = 2 пr / T �T = 2 seconds / 4 rotations =. 4 seconds per a rotation �V= 2 п (8) / (. 4) = 125. 6 m/s �So know Fc = m ac = m ( v^2 / r ) � 5 ( 125. 6 ^2 / 8) = 9765 Newton's �( I made this up, this is not realistic)

Last Problem: �A Lincoln Continental and a Yugo are making a turn. The Lincoln is four times more massive than the Yugo. If they make the turn at the same speed, then how do the centripetal forces acting upon the two cars compare. Explain.

Solution: �The centripetal force on the Continental is four times greater than that of a Yugo. According to the equation Fnet=(m • v 2) / R, force and mass are directly proportional. So 4 times the mass means 4 times the force.

Real Life Centripetal Force: