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 105 kg,
a.) What is the mass of the receiver?
1Your answer is incorrect.
b.) Calculate the kinetic energy of the tackle-receiver system before and after the collision.
I tried the formula for question a.) to set the initial and final momentum to be equal, but I keep getting the mass wrong...help?
Mt*5 m/s = (Mt + Mr)*4
(Mt+Mr)/Mt = 1 + Mr/Mt = 5/4
The receiver has only 1/4 the mass of the tackle, 26.3 kg. He should not be playing football. Are you sure you did not make a typing error?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's assume the mass of the receiver is 'm' kg. The tackle has a mass of 105 kg.
a) To find the mass of the receiver, we need to set up the equation using the principle of conservation of momentum:
Initial momentum = Final momentum
The initial momentum is the momentum of the tackle just before the collision, which is given by:
Initial momentum = mass of the tackle × velocity of the tackle
The final momentum is the momentum of the tackle-receiver system just after the collision, which is given by:
Final momentum = (mass of the tackle + mass of the receiver) × velocity after the collision
Since both the tackle and the receiver fly off horizontally at the same velocity after the collision, we can write:
mass of the tackle × velocity of the tackle = (mass of the tackle + mass of the receiver) × velocity after the collision
Substituting the given values into the equation, we have:
105 kg × 5 m/s = (105 kg + m kg) × 4 m/s
525 kg·m/s = (105 kg + m kg) × 4 m/s
Now, we can solve for the mass of the receiver 'm'. Rearranging the equation, we have:
525 kg·m/s = 4 m/s × (105 kg + m kg)
525 kg·m/s = 420 kg·m/s + 4 m/s × m kg
105 kg·m/s = 4 m/s × m kg
Dividing both sides by 4 m/s, we get:
26.25 kg = m
Therefore, the mass of the receiver is 26.25 kg.
b) To calculate the kinetic energy of the tackle-receiver system before and after the collision, we need to calculate the kinetic energy before and after the collision separately.
The kinetic energy is given by the formula:
Kinetic energy = (1/2) × mass × velocity^2
Before the collision:
- The tackle is the only object in motion, so the initial kinetic energy is given by:
Kinetic energy (before) = (1/2) × mass of the tackle × (velocity of the tackle)^2
Kinetic energy (before) = (1/2) × 105 kg × (5 m/s)^2
Kinetic energy (before) = 1312.5 joules
After the collision:
- The tackle and the receiver move together at the same velocity, so the final velocity is 4 m/s. The total mass of the system is the sum of the mass of the tackle (105 kg) and the mass of the receiver (26.25 kg).
Kinetic energy (after) = (1/2) × (mass of the tackle + mass of the receiver) × (velocity after the collision)^2
Kinetic energy (after) = (1/2) × (105 kg + 26.25 kg) × (4 m/s)^2
Kinetic energy (after) = (1/2) × 131.25 kg × 16 m^2/s^2
Kinetic energy (after) = 1050 joules
Therefore, the kinetic energy of the tackle-receiver system before the collision is 1312.5 joules, and after the collision, it is 1050 joules.
To solve question a), you can use the principle of conservation of momentum. The total momentum before the collision should be equal to the total momentum after the collision.
Let's assume the mass of the receiver is "m" kg.
Before the collision:
Initial momentum of the tackle = mass of the tackle * velocity of the tackle
Initial momentum of the receiver = mass of the receiver * 0 (since the receiver is stationary)
So, the total initial momentum before the collision is: (mass of the tackle * velocity of the tackle) + (mass of the receiver * 0)
After the collision:
Both the tackle and receiver fly off horizontally at 4 m/s, so their final velocities are the same.
Final momentum of the tackle = mass of the tackle * 4 (since the tackle is moving after the collision)
Final momentum of the receiver = mass of the receiver * 4 (since the receiver is moving after the collision)
So, the total final momentum after the collision is: (mass of the tackle * 4) + (mass of the receiver * 4)
According to the principle of conservation of momentum:
Total initial momentum = Total final momentum
Therefore, we can write the equation: (mass of the tackle * velocity of the tackle) + (mass of the receiver * 0) = (mass of the tackle * 4) + (mass of the receiver * 4)
Now, you can substitute the given values for the velocity of the tackle and the mass of the tackle and solve for the mass of the receiver.
5 * 105 = 4 * 105 + 4 * mass of the receiver
Solving this equation will give you the mass of the receiver.
For question b), to calculate the kinetic energy before and after the collision, you need to use the formula for kinetic energy:
Kinetic energy = (1/2) * mass * velocity^2
Before the collision, the tackle has a kinetic energy given by: (1/2) * mass of the tackle * (velocity of the tackle)^2
After the collision, the tackle-receiver system has a kinetic energy given by: (1/2) * (mass of the tackle + mass of the receiver) * (4)^2
You can calculate these values by substituting the known values into the respective formulas.