High School

A 324 Ns impulse was applied to an object and caused a change in its velocity of [tex]$9 \, m/s$[/tex]. What is the mass of the object?

Impulse [tex]=[/tex] Momentum

[tex](F)(t) = (M)(V)[/tex]

So, [tex]M = \frac{(F)(t)}{V}[/tex].

a) [tex]2,196 \, kg[/tex]

b) [tex]4 \, kg[/tex]

c) [tex]36 \, kg[/tex]

d) [tex]88 \, kg[/tex]

Answer :

To determine the mass of the object, we can use the relationship between impulse and momentum. The formula for impulse is given by the equation:

[tex]\[ \text{Impulse} = \text{Change in Momentum} \][/tex]

And since momentum is the product of mass and velocity, we can write:

[tex]\[ \text{Impulse} = M \times \Delta V \][/tex]

Where:
- Impulse is given as 324 Ns (Newton-seconds).
- [tex]\(\Delta V\)[/tex] is the change in velocity, which is 9 m/s.
- [tex]\(M\)[/tex] is the mass of the object, which we need to find.

We can rearrange the equation to solve for mass ([tex]\(M\)[/tex]):

[tex]\[ M = \frac{\text{Impulse}}{\Delta V} \][/tex]

Substituting the given values into the equation:

[tex]\[ M = \frac{324 \, \text{Ns}}{9 \, \text{m/s}} \][/tex]

Performing the division gives:

[tex]\[ M = 36 \, \text{kg} \][/tex]

Therefore, the mass of the object is 36 kg. The correct answer is (c) 36 kg.