Uniform Circular Motion, Work and Energy Competition A bunch of stuff you’ll see on the midterm exam

Question 1 Give the formula for speed in a circle of radius r Give the formula for centripetal acceleration Give the formula for centripetal force V = 2r Π /T a C = v 2 /r F C = mv 2 /r

…and then… How long does it take a plane, travelling at 110 m/s, to fly once around a circle of radius 2850 m? T = 160sec

…and then… The amusement park has a ride in which a person sits with his back to the inside wall of a rotating cylinder. At one instant an 83 kg person is moving at 3.2 m/s and feels a force of 560 N. What is the radius of the chamber? R = 1.51 m

…and then… What is the equation for gravitational force? What is the equation for centripetal force? If these two equations are equal to one another, what is the speed for a satellite to stay in an orbit of fixed radius? (HINT: set the two equations equal to one another and then solve for v. remember one of the masses from the gravity equation = the mass from the centripetal force equation). F G = GM 1 m/r 2, F C = mv 2 /r V = GM/r √

…and then… The Hubble telescope has helped identify a supermassive black hole (“oooh, you set my soul alight…”) in galaxy M87. Objects in orbit around it move at a speed of 7.5X10 5 m/s at a distance of 5.7X10 17 m from the center. Find the mass of the black hole. M = 4.8X10 39 kg I thought I was a fool for no one, but ooh baby i’m a fool for you, you’re the queen of the superficial and how long before you tell the truth?

…and then… What is the formula for work? What is the formula for kinetic energy? What is the formula for gravitational potential energy? What is the formula for power? W = Fdcos(θ), KE = ½ mv 2, PE = mgh, Power = work/time or energy/time

…and then… Amanda Ivey is dragging a crate along the floor. She exerts a constant force of 70 N on the crate and the rope forms an angle of 40 0 with the horizontal. If the crate travels 30m horizontally along the floor, how much work did she exert on the crate? 1608N

…and then… State the Work-Energy Theorem A constant horizontal force of 100N acts over a distance of 20 m on a 12kg crate that is initially at rest. Assuming no friction, what is the final speed of the crate? Work = KE F –KE I (100N)(20m) = 2000J = ½ mv F 2 V F 2 = 333 m 2 /s 2, so v F = m/s

…and then… A speeding car comes to a screeching halt in 65 m. If the coefficient of kinetic fiction between the tires and the road is 0.71, how fast was the car going before the driver slammed on the brakes? W = F f d = KE F –KE I -mg(0.71)(65m) = ½ mv f 2 – ½ mv i 2 V i 2 = (2)(9.8m/s 2 )(0.71)(65m) = 904 m 2 /s 2 V i = m/s = 67 m/h 0

…and then… A 5 kg cat is sitting 5 m high in a tree. What is the cat’s gravitational potential energy? After climbing down, the cat then runs at 4 m/s chasing a mouse. What is the cat’s kinetic energy? PE = mgh = (5kg)(9.8m/s 2 )(5m) = 245 J KE = ½ mv 2 = 40 J

…and then… A gymnast bounces upward on a trampoline. Her initial height is 1.2m and her max height is 4.8m, both measured with respect to the ground. Ignoring air resistance, what was the gymnast’s initial speed upwards? V 0 2 = -2g(h 0 – h f ), V 0 = 8.4 m/s

…and then… HeightKEPEE = KE + PE H0600,000J 3H/4200,000J H/4200,000J 0 An Olympic bobsled slides down a track. Ignoring friction and air resistance, fill in the table above with the correct values.

…and then… The Magnum XL-200 rollercoaster has a vertical drop of 59.4m. Assuming no friction or air resistance and assuming that the speed is approximately zero when the coaster crests the big hill, how fast is it going at the bottom? mgh F + ½ mv F 2 = mgh I + ½ mv I 2 V f = 34.1 m/s (about 76 mph)

…and then… For reasons yet to be explained, Zi Huang is pulling a toboggan for a distance of 35m along the snow with a rope directed at 250 above the ground. The tension in the rope is 94N. How much work is done by the tension? How much work would be done if the rope were parallel to the ground? 2980J 3290J

…and then… The aircraft carrier Nimitz has a fully loaded mass of 8.35 X 10 7 kg. It travels a distance of 208km in 3.5 hrs. What is the average KE of the Nimitz? V = 16.5 m/s KE = ½ mv2 = ½ (8.35 X 10 7 kg)( m 2 /s 2 ) KE = 1.1X10 10 J

…and then… When Alex Choi hits a 0.045kg golf ball, its speed is 41 m/s. How much work is done by the club? Assume that the force of the club is parallel to the motion of the ball and the club is in contact with the ball for 0.01m. What was the average force applied to the ball? 38 J 3800 N