A person of mass 60.0 kg is riding on a Ferris wheel as illustrated. Draw the free body diagram for the person when she is on the lowest position of the ride. Suppose that the wheel rotates at a speed that causes the person to experience three times her weight at that lowest point. Find the speed of the wheel under those conditions if the radius of the Ferris wheel is 6.0 m.
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- In the problems below, “little g” plays a variety of roles. Near the earth’s surface, g has a value of 9.81 m/s2. At other locations g may have different values. Solve these word problems using the data provided below. MMoon = 7.35 × 1022 kg rMoon = 1.74 × 106 m rMoon’s orbit = 3.8 x 108 m mEarth = 5.97 × 1024 kg rEarth = 6.37 × 106 m rEarth’s orbit = 1.5 x 1011 m Question 1: An astronaut is standing on the moon, holding a feather. a) Calculate the acceleration due to gravity on the moon. b) The astronaut drops the feather from a height of 2.0 meters. How long does it take the feather to hit the ground? c) The feather has a weight of 0.020 N on Earth. What is its weight on the moon?A 48 kg merry-go-round worker stands on the ride’s platform 6 m from the center. If her speed as she goes around the circle is 5 m/s, what is the force necessary to keep her from falling off the platform?You are in a carnival ride that consists of a circular room that spins around its center. You stand against the wall at the edge of the room. The room spins at a constant rate of one revolution every 5 seconds, and the room has a radius of 5 m. Your mass is 70 kg. After the room reaches it final speed, the floor drops out from beneath you, yet you remain stuck to the wall. What is the magnitude of the normal force exerted on you by the wall, and at what rate (power) does the normal force perform work on you? (Please explain the power that the normal force does work in detail.)
- 7. Snoopy is flying his vintage war plane in a "loop the loop" path chasing the Red Baron. His instruments tell him the plane is level (at the bottom of the loop) and travelling with a speed of 180 km/h. He is sitting on a set of bathroom scales, and notes that they read four times the normal force of gravity on him. What is the radius of the loop? Answer in metres.A roller-coaster car has a mass of 514 kg when fully loaded with passengers. The path of the coaster from its initial point shown in the figure to point B involves only up-and-down motion (as seen by the riders), with no motion to the left or right. Assume the roller-coaster tracks at points and are parts of vertical circles of radius r1 = 10.0 m and r2 = 15.0 m, respectively.A roller-coaster car has a mass of 500 kg when fully loaded with passengers. The car passes over a hill of radius r2 = 15.0 m, experiencing centripetal acceleration (directed toward the center). At the top of the track (point B), the car has a speed of 8.00 m/s. What is the normal force that the track exerts on the coaster at this point? {Consider Newton's law for centripetal acceleration and careful with + signs} O 4,900 N O 1,540 N O 3,550 N O 7,030 N O 2,770 N
- A roller coaster has a circular loop with a diameter (height) of 39 meters. When the coaster is upside down at the top of the loop, what is the minimum speed it must be traveling so that the passengers do not fall out?A ball is on the end of a string. The ball is being swung in a vertical circle at a constant speed. The length of the string is 1.25 m. The mass of the ball is 2.10 kg. The maximum tension the string can withstand is 61.0 N. What is the max speed of the ball without breaking the string when the ball is at the top of the circle (point a)?A bead of mass m slides without friction along a curved wire with shape z = f(r) where r = Vr2 + y², i.e. the distance from the z-axis. The wire is rotated around the z-axis at a constant angular velocity w. Gravity acts downward along the z-axis with a constant acceleration g. a) Using Newton's second law in an inertial frame, derive an expression for radius ro of a fixed circular orbit (i.e. a solution with r = ro = const.). What is the normal force the wire applies to the bead to keep it in a circular orbit? b) Show that the equation of motion for r(t) (general equation not the circular motion) is F(1 + f'(r)²) + i² f'(r)f"(r) + gf'(r) – w?r = 0. Using this verify your answer to part (a). c) Consider small displacements from the circular orbit, r = ro+e(t). Derive a condition on the function f(r) such that a circular orbit at r = ro is stable. d) Find the force on the bead in the o direction, i.e. perpendicular to the plane of wire. The angular velocity is w = . Obtain the answer…
- A "swing" ride at a carnival consists of chairs that are swung in a circle by 16.9 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 137 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair.A "swing" ride at a carnival consists of chairs that are swung in a circle by 12.4 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 135 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair.For the normal force in the drawing to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points. Suppose, for example, that the track has a radius of 2.23 m and that the driver goes past point 1 at the bottom with a speed of 24.0 m/s. What speed must she have at point 3, so that the normal force at the top has the same magnitude as it did at the bottom?