a 100g mass of cookie dough hits inelastically with a 300g mass of cookie dough and they stick. the 100 g mass was moving to the right at 40 m/s and the 300g mas was moving to the left at 5 m/s. what is the final velocity of the massive cookie dough ball? what fraction of energy is lost because of the collision?
To find the final velocity of the massive cookie dough ball, 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 consider the 100g mass of cookie dough moving to the right as positive (+), and the 300g mass of cookie dough moving to the left as negative (-).
The momentum (p) is calculated as the product of mass (m) and velocity (v): p = m * v.
Before the collision:
Momentum of the 100g mass = 100g * 40 m/s = 4000 g.m/s (+)
Momentum of the 300g mass = 300g * (-5 m/s) = -1500 g.m/s (-)
Total momentum before the collision = 4000 g.m/s + (-1500 g.m/s) = 2500 g.m/s
After the collision, the masses stick together. Let's call the final velocity of the massive cookie dough ball v_f.
The total mass of the combined cookie dough ball is now 100g + 300g = 400g.
Using the conservation of momentum, we have:
Total momentum after the collision = Total momentum before the collision
Momentum of the combined cookie dough ball = 400g * v_f
Setting up the equation:
400g * v_f = 2500 g.m/s
Now we can solve for v_f:
v_f = 2500 g.m/s / 400g
v_f ≈ 6.25 m/s
Therefore, the final velocity of the massive cookie dough ball is approximately 6.25 m/s.
To determine the fraction of energy lost because of the collision, we can use the concept of kinetic energy.
The initial kinetic energy before the collision can be calculated as:
KE_before = (1/2) * m * v^2
For the 100g mass:
KE_100g_before = (1/2) * 100g * (40 m/s)^2
KE_100g_before = 80000 g.m^2/s^2
For the 300g mass:
KE_300g_before = (1/2) * 300g * (-5 m/s)^2
KE_300g_before = 2250 g.m^2/s^2
Total initial kinetic energy before the collision: KE_total_before = KE_100g_before + KE_300g_before
KE_total_before = 80000 g.m^2/s^2 + 2250 g.m^2/s^2 = 82250 g.m^2/s^2
After the collision, the masses stick together and the final velocity is v_f ≈ 6.25 m/s.
The final kinetic energy can be calculated as:
KE_after = (1/2) * (m_total) * (v_f)^2
KE_after = (1/2) * 400g * (6.25 m/s)^2
KE_after = 7812.5 g.m^2/s^2
The fraction of energy lost can be calculated as:
Energy lost = (KE_total_before - KE_after) / KE_total_before
Energy lost = (82250 g.m^2/s^2 - 7812.5 g.m^2/s^2) / 82250 g.m^2/s^2
Energy lost ≈ 90%
Therefore, approximately 90% of the energy is lost due to the collision.