A body of mass 2kg moving with velocity of 5m/s collides with a stationary body of mas 500g. if the two bodies move together after impact. calcalate the magnitude of their common velocity
Given;
M1=2kg
U1=5m/s
M2=500g=0.5kg
U2=0m/s
V=V1+V2m/s
According to conservation of momentem,
M1U1+M2U2=M1V+M2V
M1U1+M2U2=V(M1+M2)
2*5+0.5*0=V(2+0.5)
10=V(2.5)
V=10/2.5
=4m/s
ie;V=4m/s
correct.also if were moving in opposite direction before collision.
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To calculate the magnitude of the common velocity of the two bodies after the collision, we can use the principle of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity, given by the equation:
Momentum = Mass × Velocity
According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, the first body has a mass of 2 kg and a velocity of 5 m/s. The second body has a mass of 500 g, which is equivalent to 0.5 kg, and is stationary (velocity of 0 m/s).
Therefore, the total momentum before the collision is:
Total Momentum before collision = (Mass of Body 1 × Velocity of Body 1) + (Mass of Body 2 × Velocity of Body 2)
= (2 kg × 5 m/s) + (0.5 kg × 0 m/s)
= 10 kg·m/s
After the collision, the two bodies move together with a common velocity, let's call it V.
The total momentum after the collision is:
Total Momentum after collision = (Mass of Body 1 + Mass of Body 2) × Common Velocity
= (2 kg + 0.5 kg) × V
= 2.5 kg × V
Since the total momentum before the collision must equal the total momentum after the collision, we can set up the equation:
Total Momentum before collision = Total Momentum after collision
10 kg·m/s = 2.5 kg × V
Now, we can solve for the common velocity (V) by rearranging the equation:
V = (10 kg·m/s) / (2.5 kg)
V = 4 m/s
Therefore, the magnitude of the common velocity after the collision is 4 m/s.