QUESTION 4CONNECTED PARTICLES NOTES II

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Subject: Leaving Certificate Applied MathsTeacher: Nigel MacmillanWeek: Week 12Lesson: Connected Particles Notes II

HOMEWORK QUESTIONA light pulley A is suspended from a fixed pulley.Find the acceleration of the 2Kg, 3Kg and 6Kg masses.

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Inclined planes

Example 14

A light inextensible string passes over a smooth pulley fixed at the top of a smooth inclined plane at 30 degrees to the horizontal. A particle of mass 2 kg is attached at one end of the string and hangs freely. A mass m is attached to the other end of the string and rests in equilibrium on the surface of the plane. Calculate the normal reaction between the mass m and the plane, the tension in the string and the value of m

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Example 15

A body of mass 3√3 kg on the surface of an inclined plane is acted upon by a horizontal force of 15g N, as shown in the diagram. Calculate the normal reaction of the plane on the body, and the acceleration of the body up the surface of the smooth inclined plane

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Example 16

The bodies shown are connected by a light string which passes over a smooth pulley. Calculate the tension T, the normal reaction R and the acceleration a.

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Example 17

A body of mass 5 kg is released from rest on the surface of a rough plane which is inclined at 30 degrees to the horizontal. If the body takes 2.5 seconds to acquire a speed of 4ms-1 from rest, find the resistance to motion which the body must be experiencing.

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Example 18A body of mass 8 kg is released from rest on the surface of a plane. If the resistance of motion is 1N acting on the plane and the slope of the plane is 1 in 40. calculate the acceleration of the body down the plane and the speed acquired 6 seconds after release.

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Friction

The magnitude of the maximum frictional force is a fraction of the normal reaction R. This fraction is called the coefficient of friction μ for the two surfaces in contact.

F= μRFor a perfectly smooth surface μ = 0The frictional force F is only as large as is necessary to prevent motion

Example 19

Calculate the maximum frictional force which can act when a block of mass 2 kg rests on a rough horizontal surface, the coefficient of friction between the surfaces being (a) 0.7 (b) 0.2

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Example 20

A block of mass 5 kg rests on a rough horizontal plane, the coefficient of friction between the block and the plane being 0.6. Calculate the frictional force acting on the block when the horizontal force P is applied to the block and the magnitude of P is: (a) 12N (b) 28N (c) 36NAlso calculate the magnitude of any acceleration that may occur.

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Example 21

A 10 kg van lies on a horizontal rough floor. The coefficient of friction between the van

and the floor is � . Calculate the magnitude of the force P which is necessary to pull

the van horizontally if P is applied: (a) horizontally (b) at 30o above the horizontal

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Rough inclined plane

Example 22

A mass of 6 kg rests in limiting equilibrium on a rough plane inclined at 30o to the horizontal. Find the coefficient of friction between the mass and the plane.

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HOMEWORK QUESTION

A mass of 3 kg rests on a rough plane inclines at an angle of 60o to the horizontal and μ

=� . Find the force P acting parallel to the plane which must be applied to the mass in

order to just prevent motion down the plane

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