Question

Calculate the magnitude of the linear momentum for each of the following cases

a.) a proton with mass 1.67 ×10−27 kg moving with a velocity of 6 x 106 m/s. Answer in units of kg x m/s.
b.) a 1.6 g bullet moving with a speed of 374m/s to the right. Answer in units of kg x m/s.
c.) a 8 kg sprinter running with a velocity of 11.8 m/s. Answer in units of kg x m/s.
d.) Earth (m=5.98 x 1024 kg) moving with an orbital speed equal to 29700 m/s. Answer in units of kg x m/s.

Answer 1

(a)
`p = 1.002x10^(-20)Kg.m/s`

(b)
`p = 0.598Kg.m/s`

(c)
`p = 94.4Kg.m/s`

(d)
`p = 1.77x10^(29)Kg.m/s`

Step-by-step explanation:

The linear momentum is defined as:

`p = mv` (1)

Where m is the mass and v is the velocity

a.) A proton with mass
`1.67 x10^(-27) kg` moving with a velocity of
`6 x 10^(6) m/s`.

Replacing those values in equation (1) it is gotten:

`p = (1.67x10^(-27)Kg)(6x10^(6)m/s)`

`p = 1.002x10^(-20)Kg.m/s`

So, it has a linear momentum of
`1.002x10^(-20)Kg.m/s`

b.) A 1.6 g bullet moving with a speed of 374m/s to the right.

Notice that in this case it is necessary to express the mass of the bullet in terms of kilograms:

`1.6g . (1Kg)/(1000g)` ⇒
`1.6x10^(-3)Kg`

`m = 1.6x10^(-3)Kg`

`p = (1.6x10^(-3)Kg)(374m/s)`

`p = 0.598Kg.m/s`

c.) A 8 kg sprinter running with a velocity of 11.8 m/s.

`p = (8Kg)(11.8m/s)`

`p = 94.4Kg.m/s`

d.) Earth (
`m=5.98x10^(24) kg`) moving with an orbital speed equal to 29700 m/s.

`p = (5.98x10^(24)Kg)(29700m/s)`

`p = 1.77x10^(29)Kg.m/s`