Newton's Second Law of Motion: Detail the Relationship (Research Paper Sample)

Newton’s Second Law of Motion
Name
Institution
Newton’s Second Law of Motion
Newton’s second law of motion describes how an object will change its velocity if a force is applied on it. The law explains in detail the relationship between mass, acceleration, and force with respect to a given object. This law states that if a force is applied on an object, the object will change its velocity (accelerate), and the change in the velocity will take place in the direction of the force (Taylor, 2005). For instance, if the direction of the force is in a positive direction, it will create a positive change in velocity (a positive acceleration). On the other hand, if the force is in negative direction, it will cause a negative change in velocity (retardation/negative acceleration).
In addition, the acceleration (change in velocity) of any object is directly proportional to the applied force. For instance, if the force acting on an object is tripled, the resulting acceleration will be three times greater. Contrary to this, the acceleration of any object is inversely proportional to the mass of the object. For example, if two objects are being pushed, and one object has four times more mass than the other, its acceleration will be a quarter of the other (Shipman, Wilson, Todd & Higgins, 2009).
This law can be expressed in terms of the linear momentum of a body, since the net force on a body is equal to the rate of change of its linear momentum (P). This can be illustrated as follows;
In order to express this law in terms of the objects acceleration, the mass is taken outside the differentiation operator, by assuming that it is the constant of proportionality. The expression above becomes,
Where, F= net force applied on the body, m = mass of the body, a= acceleration of the body.
Worked examples using Newton’s second law of motion
Example 1:
A lorry pulls a body of mass 10,000 kg along a straight road at a steady speed. The pulling force in the coupling between the engine and the wagon is 1000 N. The pulling force is increased by 1400 N. Assuming that the resistance to the movement of the body remains constant, the acceleration of the body can be calculated as follows.
The resultant force on the body will be given by; 1400 – 1000 = 400 N
From Newton’s second law of motion, F = ma
Therefore we have the relation; 400 = 1000 × a
Acceleration will therefore be given by; a = 400/10000
a = 0.04 mS-2
Example 2:
A force of 3500N pulls a body of mass 1000 kg. The body experiences a constant frictional force of 500 N. letting the acceleration due to gravity be, (g = 10 m S-2) work out the following;
* Draw a force diagram of the body showing the magnitude of the forces.
1000 N
3500 N
500N
10,000N
* Calculate the magnitude and direction of the resultant force on the body.
The resultant force will be given by; 3500 – 500 = 3000 N
The resultant force moves is in the direction the body was before the force was applied (to the right).
* Calculate the acceleration the body experiences,
The force acting on the body is 3000 N
Mass of the body is 1000kg
The acceleration will therefore be given by,
Acceleration = Force/ Mass = F/M
a = 3000/1000 = 3 m S-2 to the right.
Applications of Newton’s second law of motion in real life
In everyday life, Newton’s laws of motion are applied in solving various problems. For instance, Newton’s second law has helpe...