Answer to Question #84067 in Physics for Azzurra

Question #84067
A dry cleaner tosses a bag of laundry into a stationary 9.0kg cart with a horizontal velocity of 4.2m/s to the right. If the cart then begins moving at 3.0m/s to the right, how much does the bag of laundry weigh?
1
Expert's answer
2019-01-08T10:19:55-0500

We can find the weight of the bag of laundry from the law of conservation of momentum:

"m_1v_{1i} + m_2v_{2i} = (m_1 + m_2)v_f,"

here,

"m_1"

,

"m_2"

are the masses of the bag and the cart, respectively;

"v_{1i}"

,

"v_{2i}"

are the initial velocities of the bag and the cart, respectively;

"v_f"

is the final velocity of the system of cart and bag.

Then, from this equation we can find the mass of the bag,

"m_2"

:

"m_1(v_{1i} - v_f)=m_2(v_f - v_{2i}),""m_1 = \\frac{m_2(v_f - v_{2i})}{(v_{1i} - v_f)}."

Let's substitute the numbers:

"m_1 = \\frac{9 kg \\cdot (3 \\frac{m}{s} - 0 \\frac{m}{s})}{(4.2\\frac{m}{s} - 3\\frac{m}{s})} = 22.5 kg."

Finally, we can find the weight of the bag of laundry:

"W_{bag} = m_2g = 22.5 kg \\cdot 9.8 \\frac{m}{s^2} = 220 N."

Answer:

"W_{bag} = 220 N"

.

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