A 20g plastic ball is moving to the left at 30 m/s. How much work must be done th cause the ball to move to the right at 30 m/s?
0J
To cause the ball to move to the right at 30 m/s, we need to reverse its velocity. This means we need to change its direction and increase its speed to 30 m/s.
In order to calculate the work, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy of the ball while moving to the left can be calculated using the equation:
KE_initial = (1/2) * mass * velocity^2
where mass = 20g = 0.02 kg and velocity = 30 m/s.
KE_initial = (1/2) * 0.02 kg * (30 m/s)^2
= 9 J
Now, since we want the ball to move to the right at 30 m/s, we need to give it an equal amount of kinetic energy in the opposite direction.
The final kinetic energy of the ball while moving to the right is also 9 J.
Thus, the work done on the ball can be calculated as:
Work = KE_final - KE_initial
= 9 J - 9 J
= 0 J
Therefore, no work needs to be done to cause the ball to move to the right at the same speed.
To calculate the amount of work required to cause the plastic ball to move to the right at 30 m/s, we need to understand the concept of work and its formula.
Work is defined as the transfer of energy that occurs when a force acts on an object to cause its displacement. The formula for calculating work is:
Work = Force × Distance × cos(θ)
In this case, we know the mass of the plastic ball (20g) and its initial velocity to the left (30 m/s). However, we don't have enough information to calculate the force directly. We will need to determine the change in velocity and use the concept of kinetic energy.
The initial kinetic energy of the ball can be calculated using the formula:
Initial Kinetic Energy = 0.5 × mass × (initial velocity)^2
Substituting the given values:
Initial Kinetic Energy = 0.5 × 0.02 kg × (30 m/s)^2
Simplifying the equation:
Initial Kinetic Energy = 0.5 × 0.02 kg × 900 m^2/s^2
Initial Kinetic Energy = 9 Joules
Now, let's assume the ball comes to rest and then moves to the right at the same speed of 30 m/s. The final kinetic energy will also be 9 Joules (assuming no losses due to friction or other factors).
Finally, the work required to cause the ball to move to the right at 30 m/s can be calculated by subtracting the initial kinetic energy from the final kinetic energy:
Work = Final Kinetic Energy - Initial Kinetic Energy
Work = 9 J - 9 J
Work = 0 Joules
Therefore, no additional work needs to be done to cause the ball to move to the right at the same speed of 30 m/s because the initial and final kinetic energies are the same.
Work must be done to stop the ball, which would be equal to the kinetic energy of the ball, or
W1=(1/2)mv²
=(1/2)*0.02*30²
=9 J.
The same work is needed to give the ball the same kinetic energy as before, but in the opposit direction, so
W2=9 J.
The total work required is W1+W2.