A 75.0 kg fullback running east with a speed of 6.00 m/s is tackled by a 82.0 kg opponent running north with a speed of 5.00 m/s. (a) Calculate the velocity of the players immediately after the tackle. (b)Calculate the direction of the players immediately after the tackle.(c)Determine the mechanical energy that is lost as a result of the collision. (d)Where did the lost energy go?
x: m1•v1=(m1+m2) •v(x)
y: m2•v2 =(m1+m2) •v(y)
v(x)= m1•v1/(m1+m2) =75•6/(75+82)=2.87 m/s
v(y) =m2•v2 /(m1+m2)= 82•5/(75+82)=2.66 m/s
v=sqrt[v(x)²+v(y)²] =3.91 m/s
φ =arctan {v(y)/v(x)} =42.8⁰
∆K = Kf −Ki =(m1•v²/2 +m2•v²/2) - (m1 +m2) •v²/2 =
=(75•36/2 +82•25/2) –(75+82) •3.91²/2=
=1350 +1025 -1200 =1175 J
x: m•v1=(m1+m2) •v(x),
y: m•v2 =(m1+m2) •v(y),
v(x)= m•v1/(m1+m2),
v(y) =m•v2 /(m1+m2),
v=sqrt[v(x)²+v(y)²],
φ =arctan {v(y)/v(x)}.
∆K = Kf −Ki =
=(m1•v²/2 +m2•v²/2) - (m1 +m2) •v²/2.
mechanical energy -> thermal energy, sound, etc
Can you give me the values so I can compare, I don't think I am getting the right values!
Thank you!
To solve this problem, we'll use the principle of conservation of momentum. The momentum of an object is defined as the product of its mass and velocity. According to the principle of conservation of momentum, the total momentum before a collision is equal to the total momentum after the collision.
(a) Calculate the velocity of the players immediately after the tackle:
Before the tackle, the fullback and the opponent have their own momentum. The momentum of the fullback is given by:
momentum_fullback = mass_fullback * velocity_fullback
= 75.0 kg * 6.00 m/s
The momentum of the opponent is given by:
momentum_opponent = mass_opponent * velocity_opponent
= 82.0 kg * 5.00 m/s
Using the principle of the conservation of momentum, the total momentum before the tackle is equal to the total momentum after the tackle:
momentum_before_tackle = momentum_fullback + momentum_opponent
After the tackle, the total momentum becomes zero since the players come to rest and have no net motion. Therefore, we can set the total momentum after the tackle to zero:
momentum_after_tackle = 0
Setting the two equations equal to each other, we have:
momentum_fullback + momentum_opponent = momentum_after_tackle
75.0 kg * 6.00 m/s + 82.0 kg * 5.00 m/s = 0
Now, we can solve the equation to find the velocity of the players immediately after the tackle.
(b) Calculate the direction of the players immediately after the tackle:
To determine the direction, we need to consider the signs of the velocities. Since the fullback is running east, we can consider its velocity as positive. Similarly, since the opponent is running north, we can consider their velocity as positive as well.
The velocity of the players immediately after the tackle would be in a direction that satisfies the conservation of momentum equation. Since both velocities should have opposite signs due to the different initial directions, the fullback's velocity would be negative, while the opponent's velocity would be positive.
(c) Determine the mechanical energy that is lost as a result of the collision:
To determine the mechanical energy lost, we need to calculate the initial mechanical energy (before the collision) and the final mechanical energy (after the collision) and find the difference.
Initially, both players have kinetic energy. The initial mechanical energy is the sum of the kinetic energies of the fullback and the opponent, given by:
initial mechanical energy = (0.5 * mass_fullback * velocity_fullback^2) + (0.5 * mass_opponent * velocity_opponent^2)
After the tackle, both players come to rest, and their kinetic energy becomes zero. Therefore, the final mechanical energy is zero.
The mechanical energy lost as a result of the collision is the difference between the initial and final mechanical energy:
mechanical energy lost = initial mechanical energy - final mechanical energy
(d) Where did the lost energy go?
The lost mechanical energy is converted into other forms of energy during the collision. Some of the energy is dissipated as heat due to the collision, while some may be transferred to the surrounding environment as sound or potentially other forms of energy.