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5. Laws of Motion
Problem
Solution
These problems involve the consideration of Newton’s Laws of Motion:
First Law: A body remains in a state of rest or continues with uniform motion in a straight line unless it is acted upon by an external force.
Second Law: The resultant force acting on a body of constant mass is equal to the mass of the body multiplied by its acceleration.
Third Law: To every action there is an equal and opposite reaction.
Sample problem: two masses and a pulley
Two masses,  and  (where  >), are connected by a light inextensible string which passes over a pulley. (See the illustration of the physical model in Fig. 1). Write down the equations of motion and find the acceleration, a, of and the tension in the string, T. Assume there is no friction involved and ignore the mass of the pulley.
Solution
Fig. 2 illustrates the forces acting in the physical model. Using this information we can derive appropriate mathematical equations to describe the motion:
The forces acting on the system are shown in Fig. 2 where:
T = Tension in the string in Newtons
a = Acceleration of  and  in m/s2
 Force supporting the pulley system in Newtons
The equations of motion are:
For  (i)
For  (ii)
By considering these equations we can find the acceleration a and Tension, T:
Adding (i) and (ii) gives: 
Thus: 
Þ
a =  m/s2 (iii)
But, equation (ii) above gives:  . Substituting the value for a derived in equation (iii) gives:
Þ
T =  N
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