The following data concerns a tennis ball at a given instant before it is struck by a tennis racket;
horizontal momentum of tennis ball= 2.4Ns
kinetic energy of ball= 45J
a) why is correct to give the direction of the momentum but not the kinetic energy
b) write down in terms of the mass m and the velocity v of the body, expressions for
i) momentum
ii) the kinetic energy
c) use your answer to (b) to help calculate the mass and the velocity of the ball
d) when the racket hits the ball it strikes it with a constant force of 60N in a direction opposite to its momentum, ringing to rest momentarily
calulate
i)the time the tennis ball takes to stop
ii) the distance the tennis ball travels while stopping
e) the force of 60N then contiues to act on the tennis ball for a further 0.60s. calculate
i) the momentum of the ball
ii)the distance the tennis ball travels while stopping
a) It is correct to give the direction of momentum because momentum is a vector quantity that has both magnitude and direction. On the other hand, kinetic energy is a scalar quantity that only has magnitude and does not have a specific direction associated with it.
b) i) The expression for momentum is given by: momentum = mass x velocity. In this case, let's denote the mass of the tennis ball as 'm' and the velocity as 'v'. Therefore, the expression for momentum would be: momentum = m x v.
ii) The expression for kinetic energy is given by: kinetic energy = (1/2) x mass x velocity^2. Using the same variables, the expression for kinetic energy would be: kinetic energy = (1/2) x m x v^2.
c) To calculate the mass and velocity of the ball, we need additional information or equations from the problem statement. If the problem statement does not provide any further information, it would not be possible to determine the mass and velocity based on the given data alone.
d) i) To calculate the time it takes for the tennis ball to stop, we need to use the equation: force = change in momentum / time. In this case, the force acting on the tennis ball is given as 60N and it is in the opposite direction to the momentum. Since the tennis ball comes to rest, the change in momentum would be equal to the initial momentum of the ball. Therefore, we have: 60N = (2.4Ns - 0Ns) / time. Rearranging the equation, we can solve for time.
ii) To calculate the distance the tennis ball travels while stopping, we can use the equation: distance = (initial velocity x time) + (1/2) x acceleration x time^2. In this case, since the ball comes to rest, the final velocity would be 0. We already have the initial velocity and we can calculate time from part (d)i. With that information, we can calculate the distance.
e) i) To calculate the momentum of the ball when the force of 60N continues to act for 0.60s, we can use the equation: momentum = force x time. In this case, force is given as 60N and time is given as 0.60s. Plugging in these values, we can calculate the momentum.
ii) To calculate the distance the tennis ball travels while stopping, we can again use the equation: distance = (initial velocity x time) + (1/2) x acceleration x time^2. However, since the ball has already come to rest, the initial velocity is 0. We can use the value of time given in the problem statement to calculate the distance.