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

Answer:

100kg

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 $m{cart}$:

$m_{woman}+m_{cart}=\frac{M}{v} \\\\m_{cart}=\frac{M}{v} -m_{woman}$

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:

$m_{cart}=\frac{450kgm/s}{3m/s} -50kg\\\\m_{cart}=150kg-50kg\\\\m_{cart}=100kg$

the mass of the cart is 100kg.