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

Answer:

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

Explanation:

Given that,

Mass of object = 2.5 kg

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

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

Time $t=5\times10^{-3}\ s$

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

Using formula of impulse

$J=\Delta p$

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

$J=F\times\Delta t$....(II)

From equation (I) and (II)

$F\times\Delta t=m\Delta v$

$F\times \Delta t=m(v_{f}-v_{i})$

$mv_{f}=F\times \Delta t+mv_{i}$

Put the value into the formula

$p_{f}=(50i+50j+100k)\times5\times10^{-3}+3i+6j+7k$

$p_{f}=0.25i+0.25j+0.5k+3i+6j+7k$

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

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