> #mathematics , #physics > A market trolley load with shopping has a mass of 60kg.It roll across the floor at 4m/s and collide with empty trolley of mass 25kg,which was stationary.Calculate velocity of two trolley when locked ?
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Nitha Mulungu
more than 3 weeks ago

A market trolley load with shopping has a mass of 60kg.It roll across the floor at 4m/s and collide with empty trolley of mass 25kg,which was stationary.Calculate velocity of two trolley when locked ?

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C
ChatGPT
more than 3 weeks ago
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Let the initial velocity of the loaded trolley be v1 and the initial velocity of the empty trolley be 0.

The total initial momentum is:
P_initial = m1*v1 + m2*v2
P_initial = 60kg * 4m/s + 25kg * 0
P_initial = 240kg*m/s

After the collision, the two trolleys lock together and move as one unit. Let the final velocity of the combined trolleys be v_final.

The total final momentum is:
P_final = (m1 + m2) * v_final
P_final = (60kg + 25kg) * v_final
P_final = 85kg * v_final

Since momentum is conserved, we can set the initial momentum equal to the final momentum:
P_initial = P_final
240kg*m/s = 85kg * v_final

Solving for v_final:
v_final = 240kg*m/s / 85kg
v_final = 2.82 m/s

Therefore, the velocity of the two trolleys when locked together is 2.82 m/s.
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G
Google Gemini AI
more than 3 weeks ago
Momentum before collision:

Momentum of loaded trolley = mass x velocity = 60 kg x 4 m/s = 240 kg m/s

Momentum of empty trolley = mass x velocity = 25 kg x 0 m/s = 0 kg m/s

Total momentum before collision = 240 kg m/s

Momentum after collision:

Assuming the two trolleys lock together after the collision, they will have a combined mass of 60 kg + 25 kg = 85 kg.

Let v be the velocity of the two trolleys after the collision.

Momentum after collision = combined mass x velocity = 85 kg x v

Conservation of momentum:

Momentum before collision = Momentum after collision

240 kg m/s = 85 kg x v

Solving for v:

v = 240 kg m/s / 85 kg
v = 2.82 m/s

Therefore, the velocity of the two trolleys after the collision is 2.82 m/s.
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