Question

If the total momentum of a system of an old woman pushing a shopping cart is 450 kg×m/s, both with a velocity of 3 m/s, and the woman has a mass of 50 kg, what is the mass of the cart?

Answer 1

100kg

Step-by-step explanation:

Momentum is defined as the product of mass times velocity:

`p=mv`

The total momentum M must be equal to the sum of momentums of the system components, in this case the momentum of the lady plus the momentum of the cart:

`M=m_(woman)v_(woman)+m_(cart)v_(cart)`

since both the woman and the shopping cart have the same velocity:

`v_(woman)=v_(cart)=v`

the equation becomes:

`M=m_(woman)v+m_(cart)v\\M=v(m_(woman)+m_(cart))`

and since we need the mass of the cart we solve for
`m{cart}`:

`m_(woman)+m_(cart)=(M)/(v) \\\\m_(cart)=(M)/(v) -m_(woman)`

the values given by the problem are the following:

total momentum:
`M=450kgm/s`

mass of the woman:
`m_(woman)=50kg`

velocity:
`v=3m/s`

we substitute all of them in the equation to find the mass of the shopping cart:

`m_(cart)=(450kgm/s)/(3m/s) -50kg\\\\m_(cart)=150kg-50kg\\\\m_(cart)=100kg`

the mass of the cart is 100kg.