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) Think on vectors and scalars.
b)mv, 1/2 mv^2
c) 1/2 mv^2= 45j mv= 2.4Ns
solve for m, and v.
d) Impulse= change of momentum
Force(deltatime)=m(Vi- vf) where vf is
then force*distance= KE lost.
e. Force*time=change in momentum, from mv=0 to mv= final
ii makes no sense, the ball went from stop to some final velocity.
i don't get part C
solving for mv
To solve for the mass and velocity of the tennis ball, you need to use the given values of the momentum (2.4 Ns) and kinetic energy (45 J).
In part b), you have the expressions for momentum (mv) and kinetic energy (1/2 mv^2).
By equating the kinetic energy expression to 45 J, you get:
1/2 mv^2 = 45 J
From the given momentum value, you have:
mv = 2.4 Ns
Now, you can use these two equations to solve for the mass (m) and velocity (v) of the ball.
Divide the equation for momentum by mass (m):
v = 2.4 Ns / m
Substituting this value of v in the equation for kinetic energy:
1/2 m(2.4 Ns / m)^2 = 45 J
Simplifying:
(1/2) * 2.4^2 Ns^2 / m = 45 J
0.6^2 Ns^2 = m * 45 J
0.36 Ns^2 = 45 J * m
Divide both sides by 45 J:
0.36 Ns^2 / 45 J = m
0.008 Ns^2/J = m
So, you have found the mass of the tennis ball.
To find the velocity, substitute this value of m back into the equation for velocity:
v = 2.4 Ns / (0.008 Ns^2/J)
Simplifying:
v = 300 m/s
Therefore, the mass of the tennis ball is 0.008 kg and the velocity is 300 m/s.