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A crate of mass 40.0 kg is pulled by a force of 2000 N, up an inclined plane which 

makes an angle of 30º with the horizon. The coefficient of kinetic friction between the 

plane and the crate is miu.k = 0.20. If the crates starts from rest, calculate its speed after it 

has been pulled 10.0 m. Draw the free body diagram. Take 

g=10.0 ms-² .



A light arm 500m long, pivoted at its center, carries a 10kg mass at each end. If a couple of 3Nm is applied to the arm, calculate the angular acceleration produced.


Two tugs are pulling a vessel in water. Tug A is at an angle of 25º to the direction of travel and tug B is at an angle of 10º to the direction of travel. A resultant force of 150kN is produced by the two tugs. Calculate the force in the tugs ropes. 


A piano mover pushes a piano (m = 275 kg) with an applied horizontal of 1075 N. This causes the piano to accelerate, from rest, to a final velocity of 0.92 m/s over a time of 5.0 s. Calculate:

a) The acceleration of the piano.

b) The net force acting on the piano.

c) The normal force acting on the piano.

d) The coefficient of kinetic friction between the piano and the floor.


An office worker attempts to move a filing cabinet (m = 48 kg). The coefficient of static friction between the floor and the filing cabinet is 0.53.

a) Calculate the normal force acting on the filing cabinet.

b) Calculate the minimum horizontal force that the office worker must apply to the filing

cabinet to JUST move it.


A car is towing a carriage along a straight horizontal road by means of a tow-bar. The mass of the car is 1400kg and the mass of the carriage is 700kg. The non_gravitational resistances to the motion of the car and the cartiage are respectively 630N and 280N.
Given that when the car and the carriage are moving at 6m/s , the engine is working at 14.28KW, find
(a) the acceleration of the car
(b) the tension in the tow-bar
One end of a light inextensible string is fixed at a point A and a particle of mass mkg is attached to the other end B. When the particle moves in a horizontal circle of radius r below A with constant speed v m/s , the string is inclined at an angle u to the downward vertical. Show that v^2 = rgtanu.
A particle of mass mkg lies on a smooth plane inclined at an angle 30^o to the horizontal. The particle is attached to a light inextensible string which passes over a smooth pulley fixed at the top of the plane. Anothet particle of mass 3mkg is attached to the other end of the string and hangs freely. The system is released from rest with the string taught and the hanging part vertical. Find in terms of m and g,
(a) the acceleration of the system and the tension in the string
(b) the magnitude of the reaction force exerted by the string on the pulley.
One end of an inextensible string of length 3m is fastened to a fixed point O, 2m above horizontal ground. A small particle is attached to the other end of the string. The particle describes a horizontal circle 1m below O. Find in terms of g, the tension in the string and the angular velocity of the particle.
A particle P of mass 2m lies on a rough horizontal table. P is connected by a light inextensible string passing over a smooth pulley fixed at the edge of the table to another particle Q of mass 5m, hanging freely. The system is released from rest with the string taught and the hanging part vertical. If the acceleration of the system is of magnitude 4g/7, find
(a) the tension in the string
(b) the coefficient of friction between the first particle and the table.
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