A ball rolls on the horizontal floor of a tall building, then. slides off the top of a ladder (see picture) at a speed of 4 m/s. If the stair has a height h = 0.5 m and a width w = 0.3 m, on which rung of the ladder will the ball land first?
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A ball rolls on the horizontal floor of a tall building, then. slides off the top of a ladder (see picture) at a speed of 4 m/s. If the stair has a height h = 0.5 m and a width w = 0.3 m, on which rung of the ladder will the ball land first?
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- A disc with a radius of 53.89 cm is spinning at 40.6 rpm. What is the linear speed (in meters per second) of a point on the rim?In the figure, a solid 0.2 kg ball rolls smoothly from rest (starting at height H = 6.4 m) until it leaves the horizontal section at the end of the track, at height h = 2.3 m. How far horizontally from point A does the ball hit the floor?In the figure below, a solid ball rolls smoothly from rest (starting at height H = 8.3 m) until it leaves the horizontal section at the end of the track, at height h = 2.3 m. How far horizontally from point A does the ball hit the floor?
- A bicycle is turned upside down while its owner repairs a flat tire on the rear wheel. A friend spins the front wheel, of radius 0.408 m, and observes that drops of water fly off tangentially in an upward direction when the drops are at the same level as the center of the wheel. She measures the height reached by drops moving vertically (see figure below). A drop that breaks loose from the tire on one turn rises h = 54.3 cm above the tangent point. A drop that breaks loose on the next turn rises 51.0 cm above the tangent point. The height to which the drops rise decreases because the angular speed of the wheel decreases. From this information, determine the magnitude of the average angular acceleration of the wheel. rad/s2 hIn the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distanced from the right edge of the plateau. The vertical heights are h, = 3.5 cm and h2 = 1.70 cm. With what speed must the ball be shot at point P for it to land at d = 4.5 cm? BallThe platform is rotating about the vertical axis such that at any instant its angular position is 0 = 4t3/2 rad, where t is in seconds. A ball rolls outward along the radial groove so that its position is r = 0.1t³ m, where t is in seconds. Determine the magnitude of velocity of the ball (m/s) when t = 2.60 seconds.
- A particle is moving in a curved path with a constant angular velocity of 2 rads-1. Which of the following is the correct magnitude of its normal (i.e. radial) acceleration when the radius of curvature is 5 m?In the figure here, a small, solid, uniform ball is to be shot from point P so that it rolls smoothly along a horizontal path, up along a ramp, and onto a plateau. Then it leaves the plateau horizontally to land on a game board, at a horizontal distance d from the right edge of the plateau. The vertical heights are h, = 3.5 cm and h2 = 1.70 cm. With what speed must the ball be shot at point P for it to land at d = 4.5 cm? BallA 1.3 kg rock is swung in a circular path and in a vertical plane on a 1 m length string. At the top of the path, the angular velocity is 9 rad/s. What is the tension in the string at that point?
- A wheel of radius 75cm is rotating with a frequency of 3.0Hz about a fixed axis of rotation. What is the speed of a piece of chewing gum stuck to the rim?In the figure, a solid 0.1 kg ball rolls smoothly from rest (starting at height H = 6.3 m) until it leaves the horizontal section at the end of the track, at height h = 2.0 m. How far horizontally from point A does the ball hit the floor? Number UnitsA 1.3 kg rock is swung in a circular path and in a vertical plane on a 1 m length string. At the top of the path, the angular velocity is 24 rad/s. What is the tension in the string at that point?