Question

An object of mass 2.5 kg has a momentum < 3, 6, 7 > kg m/s. At this instant the object is acted on a by a force < 50, 50, 100 > N for 5 x 10-3 s . What is the momentum of the object at the end of this time interval?

Answer 1

The momentum of the object at the end is
`(3.25i+6.25j+7.5k)\ kg-m/s`

Step-by-step explanation:

Given that,

Mass of object = 2.5 kg

Momentum
`p= 3i+6j+7k`

Force
`F=50i+50j+100k`

Time
`t=5*10^(-3)\ s`

We need to calculate the momentum of the object at the end

Using formula of impulse

`J=\Delta p`

`J=m\Delta v`...(I)

`J=F*\Delta t`....(II)

From equation (I) and (II)

`F*\Delta t=m\Delta v`

`F* \Delta t=m(v_(f)-v_(i))`

`mv_(f)=F* \Delta t+mv_(i)`

Put the value into the formula

`p_(f)=(50i+50j+100k)*5*10^(-3)+3i+6j+7k`

`p_(f)=0.25i+0.25j+0.5k+3i+6j+7k`

`p_(f)=(3.25i+6.25j+7.5k)\ kg m/s`

Hence, The momentum of the object at the end is
`(3.25i+6.25j+7.5k)\ kg-m/s`