You are lawn bowling and bowl a ball with a speed of 5.00 m/s. Unfortunately, your ball hits a large rock of mass 400 g, resulting in a perfectly elastic collision. If the final velocity of the ball after the collision is -2.93 m/s, what must the mass of the ball be
To determine the mass of the ball, we can apply the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's denote the mass of the ball as "m" (to be determined) and its initial velocity as "u". The rock has a mass of 400 g (or 0.4 kg) and is initially at rest.
Before the collision, the momentum is given by:
Initial Momentum = Mass of the ball (m) * Initial velocity (u)
After the collision, the momentum is given by:
Final Momentum = Mass of the ball (m) * Final velocity (v)
According to the conservation of momentum,
Initial Momentum = Final Momentum
So, we can write the equation as:
Mass of the ball (m) * Initial velocity (u) = Mass of the ball (m) * Final Velocity (v)
Substituting the given values:
m * 5.00 m/s = m * -2.93 m/s
Now, we can cancel out the mass "m" on both sides of the equation, resulting in:
5.00 m/s = -2.93 m/s
Since the velocities are not equal, it implies that there was an error in the calculations or the assumption of an elastic collision was incorrect. In a perfectly elastic collision, the relative velocities should be equal and opposite, but that is not the case here.
Hence, it is not possible to determine the mass of the ball based on the given information and assumptions.