To find the velocity of the center of mass of the two cars, we use the formula for the velocity of the center of mass:
V_cm = (m₁v₁ + m₂v₂) / (m₁ + m₂)
where:
m₁ = 2210 kg (mass of Plymouth)
v₁ = 105 km/h (velocity of Plymouth)
m₂ = 2080 kg (mass of Ford)
v₂ = 43.5 km/h (velocity of Ford)
Step 1: Convert velocities to m/s
Since 1 km/h = 5/18 m/s, we convert the velocities:
v₁ = 105 × (5/18) = 29.167 m/s
v₂ = 43.5 × (5/18) = 12.083 m/s
Step 2: Compute the center of mass velocity
V_cm = (2210 × 29.167 + 2080 × 12.083) / (2210 + 2080)
= (644590.7 + 251326.4) / 4290
= 895917.1 / 4290
= 20.89 m/s
Step 3: Convert back to km/h
V_cm = 20.89 × (18/5) = 75.2 km/h
Final Answer:
The center of mass of the two cars is moving at 75.2 km/h.
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
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A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
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