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A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m, as

shown in Figure. A horizontal force acts on one end of the rope. Assuming that the sag is

negligible, Find the acceleration of rope and block, (c) the force on the block from the rope, and

(d) the tension in the rope at its midpoint.


The 10.2 kg block in figure is held in place by a force applied to a rope passing over two

massless, frictionless pulleys. Find the tensions T1 to T5 and the magnitude of force F.


The three ropes in figure are tied to a small, very light ring. Two of the ropes are anchored

to walls at right angles, and the third rope pulls as shown. What are T1 and T2, the magnitudes of

the tension forces in the first two ropes?


the elevators and passengers have a mass of 5500kg. After a stop at the fith floor the elevator accelerates upward uniformly at 1.0m/s^2 until it is rising at 2.0m/s


Sam, Choi, Mich, Pia, and Sheen are on a 6’ x 4’ rectangular balsa. They are having trouble in keeping the balsa balanced as they are unaware of their center of mass. Find their center of mass, given the following: Sam is at 3 feet east, and 2 feet north of the balsa’s geometric center. She weighs 78 kg.

show complete solutions. Draw a diagram and locate the points.


A 0.1 kg block, not attached to a spring, is pushed until the spring is compressed a distance of 10 cm from the equilibrium position. The block is released from rest and slides along a path that is without friction from point A to point B as shown in figure . After reaching point B, the block travels on a rough ramp of angle 45° from the ground and reaches a height h of 1 m (point C) where L = 0.707108079859474 m. Assuming a spring constant of 3112 N/m and a coefficient of kinetic friction of 0.36. A. What is the speed of the block at point B? B. What is the speed of the block at point C?

A block of m1 = 9 kg rests on a horizontal table, attached to another block of m2 = 3 kg by a light string as shown in the figure below



A. What is the minimum coefficient of static friction such that the objects remain at rest?

B. If the coefficient of static friction is less than that found in part (a), and if the coefficient of kinetic friction between the block and the table is 0.15find the time it takes for the 3kg mass to fall 4 m to the floor if the system starts from rest?


A 0.7 kg block, not attached to a spring, is pushed until the spring is compressed a distance of 10 cm from the equilibrium position. The block is released from rest and slides along a path that is without friction from point A to point B as shown in figure . After reaching point B, the block travels on a rough ramp of angle 45° from the ground and reaches a height h of 2 m (point C) where L = 1.41421615971895 m. Assuming a spring constant of 1209 N/m and a coefficient of kinetic friction of 0.57. A. What is the speed of the block at point B? (4 points) B. What is the speed of the block at point C? (6 points)
Find the relative error in estimating the volume of a cube of a side length 5 cm given that the relative error in estimating itsnlength is 0.01 then find the absolute error in this case.

An engineer measured the length of a buliding which was equal to 55.2 m . If there was an error of 0.02 m. What are probabilities of the real vaule of buliding length?


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