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Two balls, A and B, with masses ma and mb are connected by a taut, massless string, and are moving along a horizontal frictionless plane. The distance between the centers of the two balls is L. At a certain instant, the velocity of ball B has magnitude v and is directed perpendicular to the string and parallel to the horizontal plane, and the velocity of ball A is zero.

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In a car lift used in a service station, compressed air exerts a force on a small piston of circular cross section having a radius of r1 = 5.05 cm. This pressure is transmitted by an incompressible liquid to a second piston of radius 14.7 cm. What force must the compressed air exert on the small piston in order to lift a car weighing 13,300 N?

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A uniform solid disk made of wood is horizontal and rotates freely about a vertical axle at its center. The disk has radius 0.600 m and mass 1.60 kg and is initially at rest. A bullet with mass 0.0200 kg is fired horizontally at the disk, strikes the rim of the disk at a point perpendicular to the radius of the disk, and becomes embedded in its rim, a distance of 0.600 m from the axle. After being struck by the bullet, the disk rotates at 4.00 rad/s. What is the horizontal velocity of the bullet just before it strikes the disk?

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A child playing in a swimming pool realizes that it is easy to push a small inflated ball under the surface of the water whereas a large ball requires a lot of force. The child happens to have a styrofoam ball (the shape of the ball will not distort when it is forced under the surface), which he forces under the surface of the water. If the child needs to supply 608 N to totally submerge the ball, calculate the diameter ???? of the ball. The density of water is ????w=1.000×103 kg/m3, the density of styrofoam is ????foam=95.0 kg/m3, and the acceleration due to gravity is ????=9.81 m/s2.

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Now assume that the pitcher in Part D throws a 0.145-kg baseball parallel to the ground with a speed of 32 m/s in the x direction. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. What is the ball’s x-component of velocity just after leaving the bat if the bat applies an impulse of −8.4N⋅s to the baseball

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An archery bow is drawn a distance d = 0.29 m and loaded with an arrow of mass m = 0.094 kg. The bow acts as a spring with a spring constant of k = 112 N/m, and the arrow flies with negligible air resistance. To simplify your work, let the gravitational potential energy be zero at the initial height of the arrow. How fast will the arrow travel and it leave the bow?

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In this problem, you will practice applying this formula to several situations involving angular acceleration. In all of these situations, two objects of masses m1 and m2 are attached to a seesaw. The seesaw is made of a bar that has length l and is pivoted so that it is free to rotate in the vertical plane without friction. You are to find the angular acceleration of the seesaw when it is set in motion from the horizontal position. In all cases, assume that m1>m2, and that counterclockwise is considered the positive rotational direction.a) Assume that the mass of the swing bar, as shown in the figure, is negligible. Find the magnitude of the angular acceleration a(alpha) of the seesaw. Express in variables of m1, m2, l and g.b) Now consider a similar situation, except that now the swing bar itself has mass mbar . (Part C figure)

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