The figure shows a 0.3 kg baseball just before and just after it collides with a bat. Just before, the ball has velocity v→1 of magnitude 13.0 m/s and angle θ1 = 31.7∘. Just after, it is traveling directly upward with velocity v→2 of magnitude 11.5 m/s. The duration of the collision is 1.90 ms. What are the (a) magnitude and (b) direction (relative to the positive direction of the x axis) of the impulse on the ball from the bat? What are the (c) magnitude and (d) direction of the average force on the ball from the bat? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A 36.0 kg wheel, essentially a thin hoop with radius 2.10 m, is rotating at 165 rev/min. It must be brought to a stop in 25.0 s. (a) How much work must be done to stop it? (b) What is the required average power? Give absolute values for both parts. (a) Number Units (b) Number Units
The figure shows a plot of potential energy U versus position x of a 0.230 kg particle that can travel only along an x axis under the influence of a conservative force. The graph has these values: UA = 9.00 J, UC = 20.0 J and UD = 24.0 J. The particle is released at the point where U forms a "potential hill" of "height" UB = 12.0 J, with kinetic energy 6.00 J. What is the speed of the particle at (a)x = 3.50 m and (b)x = 6.50 m? What is the position of the turning point on (c) the right side and (d) the left side? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The drawing shows a skateboarder moving at 7.50 m/s along a horizontal section of a track that is slanted upward by θ = 35.0∘ above the horizontal at its end, which is 0.570 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
In the figure, a small block of mass m = 0.014 kg can slide along the frictionless loop-the-loop, with loop radius R = 11 cm. The block is released from rest at point P, at height h = 5 R above the bottom of the loop. What are the magnitudes of (a) the horizontal component and (b) the vertical component of the net force acting on the block at point Q? (c) At what height h should the block be released from rest so that it is on the verge of losing contact with the track at the top of the loop? (On the verge of losing contact means that the normal force on the block from the track has just then become zero).
The figure here shows a plot of potential energy U versus position x of a 0.884 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) Three values are UA = 15.0 J, UB = 35.0 J and UC = 45.0 J. The particle is released at x = 4.50 m with an initial speed of 7.82 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (b) magnitude and (c) direction of the force on the particle as it begins to move to the left of x = 4.00 m? Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.50 m at speed 7.82 m/s. (d) If the particle can reach x = 7.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (e) magnitude and (f) direction of the force on the particle as it begins to move to the right of x = 5.00 m? (a) Number Unit (b) Number Unit (c) (d) Number Unit (e) Number Unit (f)
A 5.0 kg block moves in a straight line on a horizontal frictionless surface under the influence of a force that varies with position as shown in the figure. The scale of the figure's vertical axis is set by Fs = 18.0 N. How much work is done by the force as the block moves from the origin to x = 8.0 m? Number Units