 # DYNAMICS :NEWTON’S LAWS OF MOTION, MOTION ALONG INCLINED PLANE AND MOTION OF CONNECTED PARTICLES (CONT)

MOTION OF CONNECTED PARTICLES

In this unit, we shall examine the motion of two or more bodies connected by a light inextensible string, connected to a light smooth pulley. The basic assumption we make is that the tensile force in the string is always the same throughout every section of the string. We can easily write down the equation of motion of the connected particles, once they are set in motion.

Example

The particles whose masses are 15kg and 12 kg respectively are attached to the ends of a light inextensible string. The string passes over a light frictionless pulley and the masses hang freely. The system is released from rest when the 15kg mass is 32m above the floor. Find:

(i)                 the tension in the string;

(ii)              the time taken by the 15kg mass to reach the floor.

The net force is T-12kg

By Newton”s 2nd law T-12kg

3g  = 27a a =g/9a = 10/9   , T – 12g  = 12a

T = 12a + 12g =12x 10/9  +12 x10  =400/3

EVALUATION

A force P acts on a body of mass 5kg on a smooth horizontal floor if it produces an acceleration of 4.5 m/s , find the magnitude of P

GENERAL EVALUATION

1) A body of mass 15kg is placed on a smooth plane which is inclined at 60 to the horizontal, find the acceleration of the body as it moves down the plane

2) A body of mass 5kg is connected by a light inelastic string which is passed over a fixed frictionless pulley by a movable frictionless pulley of mass 1kg over which is wrapped another light inelastic string which connects masses 3kg and 2kg , find the acceleration of the masses and the tension in the strings

New Further Maths Project 2  page 237- 242

WEEKEND ASSIGNMENT

A body of mass of mass 100kg is placed in a lift , find the reaction between the floor of the lift and the body when the lift moves upward

1)at constant velocity  a) 800N  b) 900N  c) 1000N  d) 600N

2)  with an acceleration of 3.5m/s   a) 100N  b) 1350N  c) 1200N  d) 1500N

3) A body of mass 20kg is placed in a lift , find the reaction between the floor of the lift and the body when the lift moves downward with a retardation of 2.5 m/s  a) 250N  b) 300N  c) 350N  d) 400N

4) Law of inertia is also known as Newton”s —– Law of motion    a)  2nd  b) 1st  c) 3rd  d) 4th

5) The relationship between force and acceleration of a body in motion can be attributed to  Newton”s  ——–  Law of motion    a) 1st  b) 2nd  c) 3rd  d) 4th

THEORY

1) A car of mass 0.9 tonnes is moved by a constant force F from a speed of 12m/s to 16m/s  over a distance of 50m, find F

2) Two masses 10kg and 8kg are connected by a light  inextensible string which is passed over a light frictionless pulley fin the tension in the string

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