Newton Second Law of Motion and Equation of Motion
Newton Second Law of Motion and Equation of Motion
The magnitude of the net force acting on a body is proportional to the product of the mass of the body and its acceleration.The direction of the force is same as that of the acceleration.
...............(i)
Here, k is a constant, m = mass and a = acceleration
In terms of momentum second law can be stated as:
The rate of change of momentum of an object is proportional to the net force applied on the object.The direction of the change of momentum is the same as the direction of the net force.
Let us see how the two ways of stating the second law are equivalent.Suppose a object of mass m is moving along a straight line with a constant acceleration a. Also, suppose its velocity at time is
, which changes to
at time
.
The linear momentum at time is
.
Here, p = momentum ,t= time and v = velocity
The rate of change of momentum is
According to the second law,
or (where k is a constant)
or
or ....................(ii)
Equation (ii) is same as that of equation (i)
Equation of motion:
1. First equation of motion:
This equation is a relation between initial velocity, final velocity and acceleration.In lots of problems, the object starts motion from the rest with zero initial velocity. In such cases if we have knowledge about two kinematics quantities we can easily find the third quantity.
2. Second equation of motion:
This equation gives relation between distance, initial velocity, time and acceleration.
3. Third equation of motion:
This equation give the relation between final velocity, initial velocity, acceleration and distance.
Application of second law of motion:
1. A cricket palyer moves his hands backward while catching a fast cricket ball.
2. During athletics meet, athletes doing high jump and long jump land on foam or a heap od sand to decrease the force on the body and the landing is comfortable.
3. When we kick a ball we apply some force in it, and in a specific direction. If applied force is more than the ball will cover a longer distance and if the applied force is less than ball wiil cover a smaller distance.
4. Pushing a empty cart is easy than pushing a loaded cart , this is because if the mass of the cart is less than force required to pull the cart will also be less.
Q 1. A 650 kg rocket is to be speed up from 440 metres per second to 520 meters per second in outer space. If the thrust of the engine is 1200 N, for how long must the engine be fired?
Solution: The change in the momentum of the rocket
= (650) (520) - (650) (440) = 52000 kg m/s.
This must be equal to the impulse, so = (1200 N) (
) = 52000 kg m/s
= 43 s
Q 2. A boy of mass 58 kg jumps with a horizontal velocity of 3 m/s onto a stationary skateboard of mass 2 kg. What is his velocity as he moves off the skateboard ?
Solution: Assume there is zero unbalanced horizontal force in the horizontal direction and that left to right is the positive (+) direction.
Momentum before interaction =
A body of mass 4 kg moving on a horizontal surface with an initial velocity of 6 m | |||
| Right Option : C | |||
| View Explanation | |||
If a constant force on a body initially kept at rest, the distance moved by the body in time t is proportional to _____________________. | |||
| Right Option : B | |||
| View Explanation | |||
The tension in the cable, when the lift of mass 150 Kg is ascending with a constant velocity, is | |||
| Right Option : C | |||
| View Explanation | |||
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