The figure shows a thin rod, of length L= 2.20 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 8.10 kg is attached to the other end. The rod is pulled aside to angle 00 = 8 and released with initial velocity V 0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if the mass is increased?

A pendulum consists of a bob of mass m and a string of constant length 1 = 63.0 cm and negligible mass. The free end of the string is attached to a fixed point A and the pendulum swings to-and-fro in a vertical plane. A 1-h speed of bob = h 30° U If the pendulum bob has a speed u = 3.10 m s¹ at the lowest point of its swing, what is the speed of the bob when the string makes an angle of 30° with the vertical, as indicated in the diagram? Give your answer by entering a number, specified to an appropriate number of significant figures, in the empty box below. 1 ms-1.

Two sticky spheres are suspended from light ropes of length L that are attached to the ceiling at a common point. Sphere A has mass 2m and is hanging at rest with its rope vertical. Sphere B has mass m and is held so that its rope makes an angle with the vertical that puts B a vertical height H above A. Sphere B is released from rest and swings down, collides with sphere A, and sticks to it. In terms of H, what is the maximum height above the original position of A reached by the combined spheres after their collision?

A proton (mass m = 1.67 × 10-27 kg) is being accelerated along a straight line at 2.70 × 1011 m/s2 in a machine. If the proton has an initial speed of 9.00 × 106 m/s and travels 5.60 cm, what then is (a) its speed and (b) the increase in its kinetic energy?

At a post office truck loading station, a small 0.2 kg package is released from rest at point A on a track that forms a quarter circle with a radius of 1.60 m. The packet is so small relative to said radius that it can be treated as a particle. The package slides along the track and reaches point B with a speed of 4.80 m/s. From here, the package slides 3.0 m on a horizontal surface to point C, where it stops. 0.21 A: R=1.60 m a)- What coefficient of kinetic friction does the horizontal surface have? -0.7281 B -3.00 m B: 0.45 m = 0.200 kg C: -0.8321 b)- How much work does friction do on the package as it slides along the circular arc between A and B? 0.39 C D: 0.835 J 0.27 D: -3.821 E: 0.30 3.28 J

An object of mass m= 7.6 kg is free to move on a horizontal surface without any friction. It is initially at rest and starts moving under a net force of F =(3N)î +(4N)ĵ . What is the object's speed in m/s after moving 1 meter?

A ball is held at rest at some height above a horizontal surface.  Once the ball is released it falls under gravity, hits the surface at time T1 , and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified. How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer. How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time Tstop? Give your answer for Tstop as a single formula that contains only two independent variables, namely p and the time T1 .

The three spheres in the figure, with masses MA = 85 g, mB = 13 g, and mc = 17 g, have their centers on a common line, with L = 22 cm and d = 3 cm. You move sphere B along the line until its center-to-center separation from C is d = 3 cm. How much work is done on sphere B(a) by you and (b) by the net gravitational force on B due to spheres A and C? B ·d- C

A particular spring has a rest length of 5.0 cm when it is not compressed, and a length of 4.5 cm when a mass of 10kg is placed on top of it. How long is the spring with the 10kg mass on top when it is taken into an elevator accelerating upwards at 1.0 m/s2​ ​?

Someone is stuck at the top of a tower, and is very thirsty. A heroic dog, weighing 40lbs, carries a bucket of water, weighing 5 lbs, up a helical staircase that encircles a tower with a radius of 15ft. The tower is 60ft high and the dog makes exactly three complete revolutions climbing to the top. Unfortunately the bucket leaks water at a steady rate, and during the ascent, 1lb of water leaks out. How much work is done by the dog against gravity?