calculate the ratio of momentum when 1.velocity of the object is doubled 2.mass of the object is halved?
To calculate the ratio of momentum when the velocity of an object is doubled and the mass of the object is halved, we can use the formula for momentum:
Momentum (p) = mass (m) × velocity (v)
Let's assume the original mass is m1 and the original velocity is v1. We can then calculate the initial momentum (p1) using these values:
p1 = m1 × v1
Now, let's calculate the momentum when the velocity is doubled. The new velocity will be 2v1:
p2 = m1 × (2v1)
Next, let's calculate the momentum when the mass is halved. The new mass will be (1/2)m1:
p3 = (1/2)m1 × v1
Lastly, we can calculate the ratio of momentum by dividing the new momentum by the initial momentum:
Ratio of momentum = p2 / p1 = (m1 × 2v1) / (m1 × v1) = 2
Ratio of momentum = p3 / p1 = ((1/2)m1 × v1) / (m1 × v1) = 1/2
Therefore, the ratio of momentum when the velocity is doubled and the mass is halved is 2:1/2, which simplifies to 4:1.