Mass A, 2.0kg , is moving with an initial velocity of 7 m/s in the +x-direction, and it collides with mass B,4.0kg , initially moving in the +x-direction. After the collision, the two objects stick together and move as one. What is the change in kinetic energy of the system as a result of the collision, in Joules?
I want to find the total initial kinetic energy, then find final velocity, and then find final kinetic energy. I got the correct answer (-42.47), but find myself unable to reproduce this result. Did I get it correct by accident? I would appreciate if you could please write which formulas should be used and which numbers get plugged in...
I thought initial kinetic energy would be (kinetic energy of object 1 + kinetic energy of object 2), and final velocity would be through (m1*v1 + m2*v2)/m1+m2. I'm pretty sure I should be getting 238 as my initial kinetic energy, but somehow I'm getting 323...why?
Thank you!
WAIT! I got it now...made a mistake.........
To calculate the change in kinetic energy of the system, you need to find the total initial kinetic energy and the final kinetic energy.
Let's break down the steps to find the correct answer:
1. Find the total initial kinetic energy:
Kinetic energy (KE) = 0.5 * mass * velocity^2
For mass A: KE_A = 0.5 * 2.0kg * (7m/s)^2 = 98 Joules
For mass B: KE_B = 0.5 * 4.0kg * (7m/s)^2 = 196 Joules
Total initial kinetic energy: KE_initial = KE_A + KE_B = 98 Joules + 196 Joules = 294 Joules
2. Find the final velocity of the combined masses:
Since the masses stick together after the collision, their velocities must combine and move together as one.
Use the equation: final velocity = (m1 * v1 + m2 * v2) / (m1 + m2)
Substituting the values:
final velocity = (2.0kg * 7m/s + 4.0kg * 7m/s) / (2.0kg + 4.0kg)
= (14kg*m/s + 28kg*m/s) / 6.0kg
= 42kg*m/s / 6.0kg
= 7m/s
3. Find the final kinetic energy:
Since the masses combine and move together with the final velocity, their final kinetic energy is calculated using the equation:
KE_final = 0.5 * total mass * (final velocity)^2
Total mass = mass A + mass B = 2.0kg + 4.0kg = 6.0kg
KE_final = 0.5 * 6.0kg * (7m/s)^2 = 0.5 * 6.0kg * 49m^2/s^2 = 147 Joules
4. Find the change in kinetic energy:
Change in kinetic energy (ΔKE) = KE_final - KE_initial
ΔKE = 147 Joules - 294 Joules = -147 Joules
It seems that your initial kinetic energy calculation of 238 Joules is incorrect. The correct value should be 294 Joules. Therefore, the correct change in kinetic energy is -147 Joules, not -42.47 Joules.
To determine the change in kinetic energy of the system, we need to follow a step-by-step approach. Let's break it down:
Step 1: Calculate the initial kinetic energy (Ki)
The initial kinetic energy is equal to the sum of the kinetic energies of both masses A and B. The formula for kinetic energy is given by:
K = 1/2 * m * v^2
Where K is the kinetic energy, m is the mass, and v is the velocity.
For mass A:
m1 = 2.0 kg
v1 = 7 m/s
For mass B:
m2 = 4.0 kg
v2 = 7 m/s
Now we can calculate the initial kinetic energy:
Ki = (1/2 * m1 * v1^2) + (1/2 * m2 * v2^2)
= (1/2 * 2.0 kg * (7 m/s)^2) + (1/2 * 4.0 kg * (7 m/s)^2)
= (1/2 * 2.0 kg * 49 m^2/s^2) + (1/2 * 4.0 kg * 49 m^2/s^2)
= (49 kg * m^2/s^2) + (98 kg * m^2/s^2)
= 147 kg * m^2/s^2
= 147 J
So the initial kinetic energy (Ki) of the system is 147 Joules.
Step 2: Calculate the final velocity (vf)
When the two masses stick together, they move as one. To find their final velocity, we can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.
The formula for momentum is given by:
p = m * v
For mass A:
m1 = 2.0 kg
v1 = 7 m/s
For mass B:
m2 = 4.0 kg
v2 = 7 m/s
Total momentum before the collision = m1 * v1 + m2 * v2
Total momentum after the collision = m_total * vf
According to the conservation of momentum, we have:
m1 * v1 + m2 * v2 = (m1 + m2) * vf
Now we can solve for vf:
vf = (m1 * v1 + m2 * v2) / (m1 + m2)
= (2.0 kg * 7 m/s + 4.0 kg * 7 m/s) / (2.0 kg + 4.0 kg)
= (14 kg * m/s + 28 kg * m/s) / 6.0 kg
= 42 kg * m/s / 6.0 kg
= 7 m/s
So the final velocity (vf) of the system is 7 m/s.
Step 3: Calculate the final kinetic energy (Kf)
The final kinetic energy is given by the formula mentioned earlier:
Kf = 1/2 * m_total * vf^2
Where m_total is the combined mass of mass A and mass B.
m_total = m1 + m2
= 2.0 kg + 4.0 kg
= 6.0 kg
Now we can calculate the final kinetic energy:
Kf = 1/2 * 6.0 kg * (7 m/s)^2
= 1/2 * 6.0 kg * 49 m^2/s^2
= 147 kg * m^2/s^2
= 147 J
So the final kinetic energy (Kf) of the system is 147 Joules.
Step 4: Determine the change in kinetic energy (ΔK)
The change in kinetic energy is calculated as:
ΔK = Kf - Ki
ΔK = 147 J - 147 J
ΔK = 0 J
Therefore, the change in kinetic energy of the system as a result of the collision is 0 Joules.