Newton's Second Law

Impluse And Momentum of Class 11

How will you catch (without braking) a raw egg moving toward you?

Obviously, you will make initial contact with the egg as far in front of your body as possible, and then move your hands backwards to bring the egg slowly to rest.

The physics of the process is simple. When the egg reaches you it has some momentum. To stop the egg you must reduce the momentum to zero by applying an impulse. That is, you must have a certain area under the F - t curve. As shown in figure (9.3), you have a choice. You can exert a large force for a short time or a small force for a long time. One way or another you must generate an area under the F - t graph equal to Δp.

The quantitative aspect of it is illustrated below.

From equation (9.6), we know

Newton's Second Law  = ΔNewton's Second Law

Using definition of Impulse, we get

Newton's Second Law= ΔNewton's Second Law

For constant net force,

Newton's Second Law= ΔNewton's Second Law

orNewton's Second Law Δt = ΔNewton's Second Law

If the force is not constant, then we can find the average force as

Newton's Second Law = Newton's Second Law

Newton's Second Law

For short intervals Newton's Second Law approximates the instantaneous force. In the limit as Δt approaches zero the fraction Newton's Second Law becomes the derivative.

Thus, Newton's Second Law = Newton's Second Law(9.7)

Equation (9.7) shows the momentum statement of the Newton's Second Law.

The net force acting on a particle is equal to the time rate of change of its linear momentum.

For a particle of constant mass equation (9.7) reduces to the common statement of Newton's Second Law.

Newton's Second Law = Newton's Second Law

orNewton's Second Law = mNewton's Second Law

Example 9.5

An 150 g ball is thrown at 30 m/s. It is struck by a bat which gives it a velocity of 40 m/s in the opposite direction. If the time of contact is 10-2s, what is the average force on the ball?

Solution

If we choose the original direction as +x axis, then

Newton's Second Law = Newton's Second Law= m(-40 i^– 30 Impulse - Momentum Theorem)

The average force is

Fav = Newton's Second LawN

Notice that this is much larger than the weight (1.5 N) of the ball.

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