a 25 kg object moving at 15 m/s collides with at 15 kg object that is standing still. They stick together and keep moving, what is their final velocity?
m1•v =(m1+m2)•u
u=m1•v/(m1+m2)
To find the final velocity of the objects after the collision, 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, assuming there are no external forces acting on the system.
The formula for momentum is given by:
Momentum (p) = mass (m) × velocity (v)
Let's calculate the total momentum before the collision:
Initial momentum of the 25 kg object = 25 kg × 15 m/s = 375 kg⋅m/s
Initial momentum of the 15 kg object (at rest) = 0 kg⋅m/s (since it is not moving initially)
The total momentum before the collision is the sum of the individual momenta:
Total initial momentum = 375 kg⋅m/s + 0 kg⋅m/s = 375 kg⋅m/s
Now, since the objects stick together and keep moving, their masses combine and we have a single object with a combined mass of 25 kg + 15 kg = 40 kg.
Let's denote the final velocity of the combined objects as Vf.
Using the principle of conservation of momentum, we equate the total initial momentum to the total final momentum:
Total initial momentum = Total final momentum
(375 kg⋅m/s) = (40 kg) × (Vf)
Now, we can solve for Vf:
Vf = (375 kg⋅m/s) / (40 kg)
Vf ≈ 9.375 m/s
Therefore, the final velocity of the combined objects after the collision is approximately 9.375 m/s.
To determine the final velocity of the two objects as they stick together and move after colliding, 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.
The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum of the 25 kg object before the collision is:
Momentum1 = mass1 * velocity1
Momentum1 = 25 kg * 15 m/s
Next, the momentum of the 15 kg object that is initially at rest is:
Momentum2 = mass2 * velocity2
Since the second object is stationary, its velocity before the collision is 0 m/s. So the momentum of the 15 kg object before the collision is:
Momentum2 = 15 kg * 0 m/s
Now, let's consider the momentum after the collision. The two objects stick together and move as one, so we can calculate the total momentum by adding their masses and velocities.
Total momentum after collision = (mass1 + mass2) * final velocity
Total momentum after collision = (25 kg + 15 kg) * final velocity
We know that the total momentum before the collision is equal to the total momentum after the collision. Therefore, we can equate the two expressions for total momentum:
Momentum1 + Momentum2 = (mass1 + mass2) * final velocity
25 kg * 15 m/s + 15 kg * 0 m/s = (25 kg + 15 kg) * final velocity
375 kg m/s = 40 kg * final velocity
Now we can solve for the final velocity:
final velocity = 375 kg m/s / 40 kg
final velocity ≈ 9.375 m/s
Therefore, the final velocity of the two objects after the collision is approximately 9.375 m/s.