In a football game, a tackle running at a constant speed of 5 m/s tackles a stationary receiver. The two fly off horizontally at 4 m/s, before they hit the ground and begin to slow down. If the mass of the tackle is 120 kg,
a.) What is the mass of the receiver?
b.) Calculate the kinetic energy of the tackle-receiver system before and after the collision.
KEsys, i = J
KEsys, f = J
Momentum is conserved.
Momentum before = MassTackle*5
momentum after =(masstackle+massreceiver)4
set them equal, you know themass of the tackle, solve for massreceiver.
To find the mass of the receiver, we can begin by using the principle of conservation of momentum. This principle states that the total momentum of an isolated system before a collision is equal to the total momentum after the collision.
Let's define the variables:
Mass of the tackle = 120 kg
Initial speed of the tackle = 5 m/s
Initial speed of the receiver = 0 m/s
Final speed after collision = 4 m/s (for both the tackle and the receiver)
Using the formula for momentum (p = m * v), we can calculate the momentum of the tackle before and after the collision:
Initial momentum of the tackle (p1) = Mass of the tackle * Initial speed of the tackle
Final momentum of the tackle (p2) = Mass of the tackle * Final speed after collision
Using the principle of conservation of momentum, we can equate the initial momentum of the tackle to the sum of the final momenta of the tackle and the receiver:
p1 = p2 (tackle) + p2 (receiver)
Now let's plug in the values:
Mass of the tackle * Initial speed of the tackle = Mass of the tackle * Final speed after collision + Mass of the receiver * Final speed after collision
We can simplify this equation by factoring out the final speed after collision:
Mass of the tackle * Initial speed of the tackle = (Mass of the tackle + Mass of the receiver) * Final speed after collision
Now we can solve for the mass of the receiver:
Mass of the receiver = (Mass of the tackle * Initial speed of the tackle) / Final speed after collision
Mass of the receiver = (120 kg * 5 m/s) / 4 m/s
Mass of the receiver = 150 kg
a.) The mass of the receiver is 150 kg.
To calculate the kinetic energy of the tackle-receiver system before and after the collision, we will use the formula for kinetic energy (KE = 1/2 * m * v^2), where m is the mass and v is the velocity.
For the tackle-receiver system before the collision, the initial kinetic energy is given by:
KEsys, i = 1/2 * (Mass of the tackle + Mass of the receiver) * Initial speed of the tackle^2
KEsys, i = 1/2 * (120 kg + 150 kg) * (5 m/s)^2
KEsys, i = 1/2 * 270 kg * 25 m^2/s^2
KEsys, i = 3375 J
Similarly, for the tackle-receiver system after the collision, the final kinetic energy is given by:
KEsys, f = 1/2 * (Mass of the tackle + Mass of the receiver) * Final speed after collision^2
KEsys, f = 1/2 * (120 kg + 150 kg) * (4 m/s)^2
KEsys, f = 1/2 * 270 kg * 16 m^2/s^2
KEsys, f = 2160 J
b.) The initial kinetic energy (KEsys, i) of the tackle-receiver system is 3375 J, and the final kinetic energy (KEsys, f) is 2160 J.