A rope passes through a small hole made on a smooth horizontal table. Two particles of equal mass are tied one at each end of the string. One of the particles hangs vertically and the other remains on the table at a distance a from the hole. The particle on the table is projected with a velocity ga perpendicular to the chord. Show that the hanging particle remains at rest. If the hanging particle is slightly disturbed in the vertical

A spacecraft cruising in space at a constant velocity of 2000 ft/s has a mass of 25,000 lbm. To slow down the spacecraft, a solid fuel rocket is fired, and the combustion gases leave the rocket at a constant rate of 150 lbm/s at a velocity of 5000 ft/s in the same direction as the spacecraft for a period of 5 s. Assuming the mass of the spacecraft remains constant, determine (a) the deceleration of the spacecraft during this 5-s period, (b) the change of velocity of the spacecraft during this time period, and (c) the thrust exerted on the spacecraft.

The initial velociies of particle one are -76 in the x-component and 151 in the y-component. The mass m1 is 10.7 kg. How do I find y-displacement.

Consider the two pucks moving on a flat, icy surface. The pucks are connected by a cord of length l. At time t = 0, a force F starts to pull the center of the cord to the right. At time t, the two pucks collide and stick together. At this time, the force has moved through a distance d, and the pucks have attained a speed v (position (b) in the figure). Assume the pucks have equal mass m, are initially at rest, the surface is frictionless, and that the cord's mass can be neglected. dCM F F m t= 0 t= t (a) What is v in terms of F, d, l, and m? V = (b) How much of the energy transferred into the system by work done by the force has been transformed to internal energy? (Use the following as necessary: F, d, e, and m.) ΔΕ, %3D int

We track the particle’s trajectory between t = 0 to t = T. During this interval, how much time transpires in the particle’s non-inertial reference frame?

Two manned  satellites approaching one another at a relative speed of 0.150M/S intend to dock. The first has a mass of 3.00×10^3 kg, the second a mass of 7.50 x 10^3 kg . Assume that the positive direction is directed from the second satellite  towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first set a lot was originally at rest. m/s ? (b) what is the loss of kinetic energy in this inelastic collision? j ? (c) repeat both parts in the frame of reference in which the second satellite was originally at rest. Final velocity m/s ? loss of kinetic energy j ? explain why the change in velocity is different in the two frames, where areas the change in kinetic energy is the same in both. I used ^ to show exponents

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Consider an object of mass 78.3kg. Assume that it’s made up of equal numbers of protons, neutrons, and electrons. Youve separated the boxes of protons and electrons by a distance of 65 m. If you were to release the clump of protons from their box, how much acceleration would the clump of protons undergo due to its attraction to the clump of electrons in the other box?

Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite. (a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.

Silid or to god o An object of mass m₁ = 4.00 kg is tied to an object of mass m2 = 4.00 kg with String 1 of length = 0.500 m. The combination is swung in a vertical circular path on a second string, String 2, of length = = 0.500 m. During the motion, the two strings are always collinear as shown in the figure. At the top of its motion, m2 is traveling at v = 4.80 m/s. Take the radial axis positive downward. (a) ( each mass. (b) What is the tension in String 1 at this instant? What is the tension in String 2 at (c) Draw the free body diagram of this instant? Which string will break first if the combination is rotated faster and faster? d) 1 m1 String 1 M DOVO dito 00101 String 2