A 1000kg space craft at 500m/s is on a collision course with a 400kg satellite travelling at 700m/s. Their paths are converging at a 45 degree angle. After the collision, they remain locked together.
a) calculate their final speed
b) calculate the quantity of non-kinetic energy that is created by the collision
a) using conservation of momentum, i found the final speed to be 518m/s.
b) because it is a completely inelastic collision, kinetic energy is not conserved so..
initial energy=final energy
sum of kinetic energy of the space craft and satellite(initial)= sum of kinetic energy final (mass of the space craft and satellite X 518m/s) + non-kinetic energy
and then solve for non-kinetic energy.. but i didn't get the right answer? can someone help me out please?
Sorry still having trouble with finding 518
To calculate the final speed, you correctly used the principle of conservation of momentum. However, I will explain the process in detail:
1. Calculate the initial momentum of the space craft and the satellite separately:
- Momentum of the space craft = mass of the space craft × velocity of the space craft
- Momentum of the satellite = mass of the satellite × velocity of the satellite
2. Since the paths are converging at a 45-degree angle, the momentum in the direction perpendicular to the initial motion direction will cancel out.
3. Use the principle of conservation of momentum to find the total momentum before the collision:
- Total initial momentum = momentum of the space craft + momentum of the satellite
4. After the collision, the space craft and the satellite will move together as one object. This means they will share the same final velocity.
5. Use the principle of conservation of momentum to find the total momentum after the collision:
- Total final momentum = (mass of the space craft + mass of the satellite) × final velocity
Now, let's calculate the final speed using the above steps:
Given:
Mass of the space craft (m1) = 1000 kg
Velocity of the space craft (v1) = 500 m/s
Mass of the satellite (m2) = 400 kg
Velocity of the satellite (v2) = 700 m/s
1. Calculate the initial momentum:
Momentum of the space craft = (m1 × v1) = (1000 kg × 500 m/s) = 500,000 kg·m/s
Momentum of the satellite = (m2 × v2) = (400 kg × 700 m/s) = 280,000 kg·m/s
2. Cancel out the momentum in the perpendicular direction (45-degree angle) to get the resultant momentum:
Resultant initial momentum = (500,000 kg·m/s) × cos(45°) = 500,000 kg·m/s × (1/√2) = 353,553 kg·m/s
3. Apply the conservation of momentum principle to find the total momentum after the collision:
Total final momentum = (m1 + m2) × final velocity = (1000 kg + 400 kg) × final velocity = 1400 kg × final velocity
Since the space craft and satellite remain locked together after collision, their total final momentum should be equal to the resultant initial momentum:
1400 kg × final velocity = 353,553 kg·m/s
Divide both sides by 1400 kg:
final velocity = 353,553 kg·m/s / 1400 kg
final velocity ≈ 252.539 m/s
So, the final speed (or velocity) after the collision is approximately 252.539 m/s.
Now, let's move on to part b) to calculate the non-kinetic energy created by the collision.
As you mentioned correctly, because it is a completely inelastic collision, kinetic energy is not conserved. Kinetic energy is converted into other forms of energy, such as deformation, heat, or sound.
The initial kinetic energy before the collision is the sum of the kinetic energy of the space craft and the satellite:
Initial kinetic energy = (1/2) × mass of the space craft × (velocity of the space craft)² + (1/2) × mass of the satellite × (velocity of the satellite)²
After the collision, the system will have a non-kinetic energy component and a final kinetic energy component. So, we have the equation:
Initial kinetic energy = final kinetic energy + non-kinetic energy
To calculate the quantity of non-kinetic energy, substitute the known values into the equation and solve for non-kinetic energy:
Initial kinetic energy = [(1/2) × 1000 kg × (500 m/s)²] + [(1/2) × 400 kg × (700 m/s)²]
Final kinetic energy = (1/2) × (1000 kg + 400 kg) × (252.539 m/s)²
Initial kinetic energy = final kinetic energy + non-kinetic energy
Now, let's do the calculations for part b):
[(1/2) × 1000 kg × (500 m/s)²] + [(1/2) × 400 kg × (700 m/s)²] = (1/2) × (1000 kg + 400 kg) × (252.539 m/s)² + non-kinetic energy
Simplify the equation:
(1/2) × 1,250,000 kg·m²/s² + (1/2) × 196,000 kg·m²/s² = (1/2) × 1,400 kg × (252.539 m/s)² + non-kinetic energy
625,000 kg·m²/s² + 98,000 kg·m²/s² = 176,449.7 kg·m²/s² + non-kinetic energy
723,000 kg·m²/s² = 176,449.7 kg·m²/s² + non-kinetic energy
Subtract 176,449.7 kg·m²/s² from both sides:
723,000 kg·m²/s² - 176,449.7 kg·m²/s² = non-kinetic energy
Non-kinetic energy = 546,550.3 kg·m²/s²
Therefore, the quantity of non-kinetic energy created by the collision is approximately 546,550.3 kg·m²/s².