A bowling ball of mass 3.5 kg moves in a
straight line at 4.48 m/s.
How fast must a Ping-Pong ball of mass
3.456 g move in a straight line so that the two balls have the same momentum?
Answer in units of m/s.
To find the required speed of the Ping-Pong ball, we can use the principle of conservation of momentum. The momentum of an object is given by the product of its mass and velocity.
Given:
Mass of the bowling ball (m1) = 3.5 kg
Velocity of the bowling ball (v1) = 4.48 m/s
Let the mass of the Ping-Pong ball be m2, and its velocity be v2.
We know that momentum is conserved, so the momentum of the bowling ball and Ping-Pong ball before the collision should be equal.
The momentum of the bowling ball (p1) is given by:
p1 = m1 * v1
The momentum of the Ping-Pong ball (p2) is given by:
p2 = m2 * v2
According to conservation of momentum, p1 = p2.
Therefore, we can say:
m1 * v1 = m2 * v2
Substituting the given values:
3.5 kg * 4.48 m/s = (3.456 g / 1000 kg) * v2
Simplifying the equation:
15.68 kg m/s = 0.003456 kg * v2
Dividing both sides by 0.003456 kg:
15.68 kg m/s / 0.003456 kg = v2
The required speed of the Ping-Pong ball is:
v2 = 4530.556 m/s
Therefore, the Ping-Pong ball must move at a speed of approximately 4530.556 m/s in order to have the same momentum as the bowling ball.
To find the velocity of the Ping-Pong ball that would result in the same momentum as the bowling ball, we can use the principle of conservation of momentum.
The momentum of an object is calculated by multiplying its mass (m) by its velocity (v). In this case, we want to find the velocity (v_p) of the Ping-Pong ball that would give it the same momentum as the bowling ball.
1. Let's calculate the momentum of the bowling ball:
Momentum_of_bowling_ball = mass_of_bowling_ball * velocity_of_bowling_ball
= 3.5 kg * 4.48 m/s
= 15.68 kg•m/s
2. Now, let's calculate the velocity of the Ping-Pong ball using the momentum of the bowling ball:
Momentum_of_PingPong_ball = mass_of_PingPong_ball * velocity_of_PingPong_ball
Since the momentum of both balls must be equal, we can set up the equation:
Momentum_of_bowling_ball = Momentum_of_PingPong_ball
Substituting the given values:
15.68 kg•m/s = (3.456 g) * velocity_of_PingPong_ball
Note: The mass of the Ping-Pong ball needs to be converted to kilograms by dividing it by 1000 since 1 kg = 1000 g.
Rearranging the equation and solving for the velocity_of_PingPong_ball:
velocity_of_PingPong_ball = 15.68 kg•m/s / (3.456 * 10^-3 kg)
Now, let's compute the velocity_of_PingPong_ball:
velocity_of_PingPong_ball = 15.68 / 0.003456
velocity_of_PingPong_ball ≈ 4531.94 m/s
Therefore, the Ping-Pong ball must move at approximately 4531.94 m/s in a straight line in order to have the same momentum as the bowling ball.
3.5*4.48=.03456*V
solve for V