A sphere moves down a rough incline. Which of the following quantities increase? O angular velocity O total energy O potential energy O linear momentum
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- In the game of tetherball a rope with length ?=1.50 m connects a ball with mass ?=0.750 kg to the top of a vertical pole so that the ball can spin around the pole as shown in the figure. What is the speed ? of the ball as it rotates around the pole when the angle ? of the rope is 38.0∘ with the vertical?A planet orbits its star in an elliptical orbit. Which of these quantities do not change as the planet orbits? O None of these quantities change as the planet orbits. O All of these quantities change as the planet orbits. O The planet's angular momentum O The planet's potential energy O The planet's kinetic energyTwo stars are orbiting around their center of mass as shown below. Find the speed of the stars. 8 R = 4 x 10° km m = 2.00 x 10 30 kg
- to expand the conservation of energy and use it to derive an equation below (Equation 5) for I in terms of g, h, m, r, and v: Given: g = gravitational acceleration h = total vertical drop of can as it rolls diagonally down the incline m = mass of the can r = radius of the can v = final linear velocity of the rolling can Requested: I = angular inertia implied by the can’s motion Equations: UGo = m g h = KT + KR [Equation 2] KT = ½ m v 2 KR = ½ I KT = ½ m v2 KR = ½ I w2 v = w rA very long way from the planet Mars (at R= c0), a martian flying saucer has run out of fuel and its kinetic energy is zero. If you assume that only the gravitational force of Mars were to act on it (i.e., neglect the forces from the sun and other solar system objects), the spacecraft would eventually crash back to the surface of Mars. The mass of Now find the flying saucer's speed when its distance from the center of Mars is R= aRm where the coefficient a > 1. Express the speed in terms of Um and a. • View Available Hint(s) Mars is Mm and its radius is Rm. Neglect air resistance throughout this problem, since the spacecraft is primarily moving through the near vacuum of space. ? K ф IT Σ Ф Ω V. m Va = Va 圓As shown below, a bullet of mass m and speed v is fired at an initially stationary sphere. The bullet goes through the sphere, and exits with a speed of. The sphere is attached to a rigid pole of 6 length L and negligible mass. What is the minimum value of v such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the sphere.) 12M√gl 5m v/6 Ⓡ Use conservation of energy to determine the speed of the sphere immediately after collision. Assume that at the top of the swing the sphere is momentarily at rest, so its kinetic energy is zero. Then apply conservation of momentum to find the initial minimum speed of the bullet.
- (4) C s) In class, we calculated the minimum speed needed by a ball to maintain contact with the track at the top of a loop-the-loop. In this problem, I want you to calculate the minimum speed the ball must have at the bottom of the loop so it maintains contact at the top. Express your answer in terms of m (the mass of the ball), g, and R (the radius of the loop). v=2Thomas Bradshaw invented the first Merry-Go-Round to be operated by a steam engine. If the engine suddenly stopped, and the Merry Go Round experienced no friction or air resistance, how could the riders on the ride slow its rotational motion? Run toward the edge of the platform. Run toward the center of the platform. Jump off the ride all at once. Lay down flat on the platform.A small mass m is released from rest at the top of a frictionless spherical surface. At what angle with vertical will it leave contact with the sphere? (48.2°)