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0.2 Force, momentum and impulse  (Page 23/35)

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Momentum and impulse

Momentum is a physical quantity which is closely related to forces. Momentum is a property which applies to moving objects.

Momentum

Momentum is the tendency of an object to continue to move in its direction of travel. Momentum is calculated from the product of the mass and velocity of an object.

The momentum (symbol p ) of an object of mass m moving at velocity v is:

p = m · v

According to this equation, momentum is related to both the mass and velocity of an object. A small car travelling at the same velocity as a big truck will have a smaller momentum than the truck. The smaller the mass, the smaller the velocity.

A car travelling at 120 km · hr - 1 will have a bigger momentum than the same car travelling at 60 km · hr - 1 . Momentum is also related to velocity; the smaller the velocity, the smaller the momentum.

Different objects can also have the same momentum, for example a car travelling slowly can have the same momentum as a motor cycle travelling relatively fast. We can easily demonstrate this. Consider a car of mass 1 000 kg with a velocity of 8 m · s - 1 (about 30 km · hr - 1 ). The momentum of the car is therefore

p = m · v = ( 1000 kg ) ( 8 m · s - 1 ) = 8000 kg · m · s - 1

Now consider a motor cycle of mass 250 kg travelling at 32 m · s - 1 (about 115 km · hr - 1 ). The momentum of the motor cycle is:

p = m · v = ( 250 kg ) ( 32 m · s - 1 ) = 8000 kg · m · s - 1

Even though the motor cycle is considerably lighter than the car, the fact that the motor cycle is travelling much faster than the car means that the momentum of both vehicles is the same.

From the calculations above, you are able to derive the unit for momentum as kg · m · s - 1 .

Momentum is also vector quantity, because it is the product of a scalar ( m ) with a vector ( v ).

This means that whenever we calculate the momentum of an object, we need to include the direction of the momentum.

Khan academy video on momentum - 1

A soccer ball of mass 420 g is kicked at 20 m · s - 1 towards the goal post. Calculate the momentum of the ball.

  1. The question explicitly gives

    • the mass of the ball, and
    • the velocity of the ball

    The mass of the ball must be converted to SI units.

    420 g = 0 , 42 kg

    We are asked to calculate the momentum of the ball. From the definition of momentum,

    p = m · v

    we see that we need the mass and velocity of the ball, which we are given.

  2. We calculate the magnitude of the momentum of the ball,

    p = m · v = ( 0 , 42 kg ) ( 20 m · s - 1 ) = 8 , 4 kg · m · s - 1

  3. We quote the answer with the direction of motion included, p = 8,4 kg · m · s - 1 in the direction of the goal post.

A cricket ball of mass 160 g is bowled at 40 m · s - 1 towards a batsman. Calculate the momentum of the cricket ball.

  1. The question explicitly gives

    • the mass of the ball ( m = 160 g = 0,16 kg), and
    • the velocity of the ball ( v = 40 m · s - 1 )

    To calculate the momentum we will use

    p = m · v

    .

  2. p = m · v = ( 0 , 16 kg ) ( 40 m · s - 1 ) = 6 , 4 kg · m · s - 1 = 6 , 4 kg · m · s - 1 in the direction of the batsman

The Moon is 384 400 km away from the Earth and orbits the Earth in 27,3 days. If the Moon has a mass of 7,35 x 10 22 kg, what is the magnitude of its momentum if we assume a circular orbit?

  1. The question explicitly gives

    • the mass of the Moon (m = 7,35 x 10 22 kg)
    • the distance to the Moon (384 400 km = 384 400 000 m = 3,844 x 10 8 m)
    • the time for one orbit of the Moon (27,3 days = 27,3 x 24 x 60 x 60 = 2,36 x 10 6 s)

    We are asked to calculate only the magnitude of the momentum of the Moon (i.e. we do not need to specify a direction). In order to do this we require the mass and the magnitude of the velocity of the Moon, since

    p = m · v

  2. The magnitude of the average velocity is the same as the speed. Therefore:

    s = d Δ t

    We are given the time the Moon takes for one orbit but not how far it travels in that time. However, we can work this out from the distance to the Moon and the fact that the Moon has a circular orbit. Using the equation for the circumference, C , of a circle in terms of its radius, we can determine the distance travelled by the Moon in one orbit:

    C = 2 π r = 2 π ( 3 , 844 × 10 8 m ) = 2 , 42 × 10 9 m

    Combining the distance travelled by the Moon in an orbit and the time taken by the Moon to complete one orbit, we can determine themagnitude of the Moon's velocity or speed,

    s = d Δ t = C T = 2 , 42 × 10 9 m 2 , 36 × 10 6 s = 1 , 02 × 10 3 m · s - 1 .

  3. The magnitude of the Moon's momentum is:

    p = m · v = ( 7 , 35 × 10 22 kg ) ( 1 , 02 × 10 3 m · s - 1 ) = 7 , 50 × 10 25 kg · m · s - 1
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Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
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