State the quantity represented by the area under the graph. (ii) When a tennis player strikes a ball he/she 'follows through in order to keep the racquet in contact with the ball for a long time. Explain. (iii) A tennis ball of mass 53.0 g initially at rest was acted upon by a force of 200 N for a time of 0.060 s. Calculate its velocity after impact. (iv) After the impact, total momentum is conserved. Comment validity of this statement.
(i) The quantity represented by the area under the graph is the integral of the function being graphed. It could represent various quantities depending on the specific context of the graph.
(ii) When a tennis player follows through in order to keep the racquet in contact with the ball for a long time, it allows for a longer duration of force exertion on the ball. This increases the impulse applied to the ball, which in turn increases its change in momentum. By extending the contact time, the player can exert a greater force and thus increase the ball's final velocity.
(iii) To calculate the velocity after impact, we can use the equation for impulse:
Impulse = Force * Time = Change in Momentum
The impulse applied to the ball is given by:
Impulse = Force * Time = 200 N * 0.060 s = 12 N∙s
Since the change in momentum equals the impulse:
Change in Momentum = Mass * Final Velocity - Mass * Initial Velocity
Rearranging the equation:
Final Velocity = (Change in Momentum + Mass * Initial Velocity) / Mass
Plugging in the given values:
Final Velocity = (12 N∙s + 0.053 kg * 0 m/s) / 0.053 kg
Final Velocity = (12 N∙s) / 0.053 kg ≈ 226.42 m/s
The velocity after impact is approximately 226.42 m/s.
(iv) The statement that total momentum is conserved after the impact is valid. According to the law of conservation of momentum, the total momentum of a system remains constant if no external forces act upon it. In this case, since no external forces are mentioned, the total momentum of the system (Tennis ball + any other objects involved) should be conserved before and after the impact.
(i) The quantity represented by the area under the graph depends on the context and the units used. Without further information about the graph, it is not possible to determine the specific quantity.
(ii) When a tennis player follows through during a stroke, it allows the racquet to remain in contact with the ball for a longer period of time. This extended contact time enables the player to transfer more momentum to the ball, resulting in a more powerful shot. It also enhances control and accuracy by allowing the player to make adjustments during the stroke.
(iii) To calculate the velocity of the tennis ball after impact, we can use the equation of motion:
Final velocity (v) = Initial velocity (u) + (Force (F) x Time (t)) / Mass (m)
Given:
Mass of the tennis ball (m) = 53.0 g = 0.053 kg
Force (F) = 200 N
Time (t) = 0.060 s
Plugging the values into the equation, we have:
v = 0 + (200 N x 0.060 s) / 0.053 kg
v = (12 Ns) / 0.053 kg
v ≈ 226.415 m/s (rounded to three decimal places)
Therefore, the velocity of the tennis ball after impact is approximately 226.415 m/s.
(iv) The statement that total momentum is conserved after the impact is valid. According to the law of conservation of momentum, the total momentum of a closed system remains constant if no external forces act on it. In the context of the tennis ball being struck, the impact only involves internal forces between the ball and the tennis racket. Since no external forces are involved, the total momentum before the impact should be equal to the total momentum after the impact.