(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.
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.
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