Theory

Newton’s Laws of Motion

The basis of mechanics revolves around the three fundamental principles known as Newton’s laws of motion.

Newton’s First Law states that - “Every body continues in its state of rest or uniform motion in a straight line unless it is acted upon by an external unbalanced force”

The first law introduces us to the concepts of force, mass and inertia.

Force: Force can be described either as a push or a pull. If we push any object then we exert a force on it. Friction is also a force, which acts, in an opposite direction to the motion thereby creating a drag and reducing the acceleration.

Mass: Mass is the amount of matter in a body. A cricket ball has more mass than a table tennis ball. The mass of an object can also be described as a measure of the object’s resistance to a change in its velocity. For e.g. a car comprising of seated people is more difficult to push than an empty car as the car and its passengers is more massive than an empty one.

Inertia: Inertia is a property of a body to maintain its state or rest or of uniform motion in a straight line. In other words, because of inertia, a body at rest continues to be at rest and a body moving continues to move with uniform velocity. To overcome inertia of a body, you have to apply some force on the body, which will change its state. It is because of inertia that when travelling in a bus you tend to move forward when it suddenly brakes to a halt. This happens because while the bus is in motion, both you and the bus are moving with the same speed. When the bus suddenly comes to a halt, because of inertia, you still continue to move as before and therefore you are thrown in front.

Newton’s Second Law of Motion states — The rate of change of momentum of a body is directly proportional to the total force acting on it and takes place in the direction of the force.
The same law can also be rephrased as - The acceleration of an object is proportional to the net force exerted on the object. In other words, greater the force applied, greater is the acceleration of the body, since the mass of a body does not change.

Force = k x Mass x Acceleration

Where k is a constant whose value depends on the unit chosen for describing the force. The SI unit of force is Newton (N) and is defined as

1N = 1 kg x 1 m/s2 (k is taken as 1)

The above equation is a summation of the first two laws of motion for a body of constant mass. It lets you find acceleration of an object for a given force and also indicates that if the force is zero then the acceleration will also be zero.

The Activity

newtons_second_law_1
 
Inter-connected Two Mass-Pulley System

This activity mainly demonstrates Newton’s second law. It lets the user observe the how the acceleration of a body is affected by the changes in the applied force, as discussed in Newton’s second Law. The activity consists of two bodies of variable masses, connected to each other with a string moving over a pulley. It is assumed that the mass of the pulley is not significant and therefore the effects of its rotation are negligible. One body hangs vertically from one end of the string, while the other body rests on a plane, whose slope with the horizontal can be changed by the user.

The magnitude and the direction of the motion of the two bodies depend on their masses, the angle of the plane with the horizontal and the coefficient of friction. The body A, because of its weight creates a corresponding force known as tension (FT) in the string attached to it. Similarly body B also creates tension, F’T, in the string. Since the string is a single body connected to both the masses, the tension is uniform throughout, i.e. FT = F’T.

As explained in the laws of motion, a body moves (accelerates) if there is external unbalanced force acting on it. In case of the body B hanging from the string, there are only two forces acting on it — the tension in the string and its own weight. The tension in the string depends on both — body A and body B. The body B will move downwards if its weight is more than the tension in the string and vice versa. Since the body B is also connected to body A by the string, the body A will also pulled towards body B as it moves downwards.

Unlike body B, body A is resting on a surface and therefore there are four forces acting on the body — its own weight (mA.g), normal force exerted by the surface on the body (FN), the tension in the string (FT) and the frictional resistance offered by the surface. When the body is resting on a horizontal plane, the only forces that can affect it are the tension in the string and the frictional force, because the weight of the body and the normal force balance out each other.

When the surface is inclined at a particular angle, then the normal force is not equal to the weight of the body and therefore the angle of inclination also starts affecting the movement of body A. By changing the mass of the body A or the angle of inclination of the plane, you can change the tension in the string. In such a system, when the tension of the string is more than the weight of the body B, it now starts moving away from the body B pulling body B along with it. The actual working of the system can be best understood by observing the tension created in the string by the changes in the masses of the two bodies and the angle of inclination.

By default the surface on which body A moves is assumed to be frictionless (coefficient of friction = 0). If we take the friction into account, then the frictional force acts in the direction opposite to the motion of the body. It will therefore require more force to move a body than it would, to move it on a frictionless surface.

Formula

The equations of the system are given as:

newtons_second_law_1
 
newtons_second_law_2
 
     
     
     


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Theory | Formula
Instructions

This exploriment requires Adobe Shockwave plug-in. Download & install only if you do not see the exploriment on the left.

This interactive lab aims to provide insights into Newton's Second Law of Motion.

The activity consists of two inter-connected masses in a mechanical system. Change the masses, surface angle and see how the forces acting on the two bodies change, in turn affecting the acceleration.

Procedure
Set the mass of body A and body B.

Set the angle of the plane on which the body A rests, by dragging the red coloured arrow icon on the upper left edge of the plane.

By default the friction factor is set to zero.

Once the parameters are set as desired, click on the 'Start' button to run the activity.

You can change input parameters even when the activity is running and observe the effects in real-time.

The numerical output of the various properties is given on the right side, as well as in form of force diagrams or free body diagrams for the two bodies.

NOTE:
The negative sign for the acceleration value indicates that the body is moving towards the left direction, while the positive value of acceleration denotes that the body is moving towards right. The negative sign does NOT denote negative acceleration, i.e. retardation.

Tips
First observe the system when the plane on which body A rests is horizontal.

In subsequent runs, you can vary the angle, the masses and observe the results.

Observe the values of the tension in the string and the weight of body B displayed next to the free body diagrams on the screen.

If the weight of body B is more than that of the tension in the string, the body B will move down pulling body A along with it. If the tension is more than the weight of body B, the body A will move towards the left pulling body B along with it.

Run the activity as many times as you want to with different inputs and try to draw your conclusions about the concept by observing the results. For more information, check out the 'Theory' section.