Home >> Mechanics, momentum & impulse, impulse

Momentum

Momentum is by definition the product of mass and velocity. So strictly speaking momentum is a vector quantity.

momentum = mass(kg) x velocity(ms^-1)

Hence the unit of momentum is (kg.ms^-1).

Impulse of a force (J)

This is simply the product of the applied force(F) acting on a body and the time(t) the force acts.

We can obtain an expression for this in terms of momentum from Newton's Second Law equation F = ma, where the force F is constant.

Remembering that velocity, force and therefore impulse are vector quantities.

For a mass m being accelerated by a constant force F, where the impulse is J , v₁ is initial velocity and v₂ is final velocity:

Ft = m(v₂- v₁)

J = Ft

J = m(v₂- v₁)

Units

Since impulse is the product of force and time:

impulse = (Newtons) x (seconds), or N.s

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Vector problems

Vector type questions on impulse are solved by first calculating the change in momentum.

This gives a vector expression for the impulse.

Using Pythagoras, the magnitude of the impulse can then be found.

The anglular direction is calculated from the coefficients of unit vectors i and j.

Example #1

A particle of mass 0.5 kg moves with a constant velocity of    (3i + 5j) m.s^-1 .

After being given an impulse, the particle then moves off with a constant velocity of (2i - 3j) m.s^-1 .

Calculate:

i)   the impulse
ii)  the magnitude of the impulse( to 2 d.p.)
iii) the direction of the impulse(θ degrees to the x-axis)

i)

ii)

magnitude of impulse = √ [( 0.5)² + (-4)² ] = √ [16.23]

= 4.03 N.s

iii)

direction tan^-1 θ = (4)/(0.5) = 8

θ = 82.8749^o = 82.87^o (2 d.p.) clockwise to the x-axis

Example #2

A particle of mass 2.5 kg is moving with a constant velocity of    (2i + j) m.s^-1 .

After an impulse, the particle moves with a constant velocity of (4i + 3j) m.s^-1 .

Calculate:

i)   the impulse
ii)  the magnitude of the impulse( to 2 d.p.)
iii) the angle(θ^o) the impulse makes with the x-axis

i)

ii)

magnitude of impulse = √ [( 5)² + (5)² ] = √ [50] = 7.07 N.s

iii)

direction tan^-1 θ = (5)/(5) = 1

θ = 45^o anticlockwise to the x-axis

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