a 75 kg object traveling at 4 m/s collides with and sticks to a 125 kg object initially at rest, what is the final velocity of the two objects?
initial momentum = 75 * 4
final momentum = (75+125) * v ===== in same direction
but we all know, momentum is the same before and after
so
v = (75*4) / (75+125)
Well, isn't that a sticky situation! When two objects collide and stick together, we can use the law of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.
So, let's calculate the initial momentum. The momentum of the first object is mass (m1) times velocity (v1), which would be 75 kg multiplied by 4 m/s. The momentum of the second object is zero since it's initially at rest.
Now, after the collision, the two objects stick together, so they become one big combined object. The final momentum of this combined object is given by the total mass (m1 + m2) times the final velocity (v_final).
To calculate the final velocity, we can equate the initial and final momentum equations:
(m1 x v1) + (m2 x 0) = (m1 + m2) x v_final
Plugging in the values, we have:
(75 kg x 4 m/s) + (125 kg x 0) = (75 kg + 125 kg) x v_final
Simplifying the equation, we have:
(300 kg m/s) = (200 kg) x v_final
Dividing both sides by 200 kg, we find:
v_final = (300 kg m/s) / (200 kg)
And voila! The final velocity of the two objects when they stick together is 1.5 m/s.
To find the final velocity of the two objects after the collision, we can use the law of conservation of momentum.
The law of conservation of momentum states that the total momentum before the collision must be equal to the total momentum after the collision, assuming there are no external forces acting on the system.
The momentum of an object is given by the product of its mass and velocity (p = m * v).
Let's denote the velocity of the 75 kg object before the collision as v1, the velocity of the 125 kg object before the collision as v2, and the final velocity of the two objects after the collision as vf.
According to the problem, the 75 kg object is traveling at 4 m/s, and the 125 kg object is initially at rest (v2 = 0).
Before the collision:
Momentum of the 75 kg object = m1 * v1
Momentum of the 125 kg object = m2 * v2 = 125 kg * 0 = 0
Total momentum before the collision = m1 * v1 + m2 * v2 = 75 kg * 4 m/s + 0 = 300 kg * m/s
After the collision:
Total momentum after the collision = (m1 + m2) * vf = (75 kg + 125 kg) * vf = 200 kg * vf
Since we have the conservation of momentum, we can set the total momentum before the collision equal to the total momentum after the collision:
300 kg * m/s = 200 kg * vf
Simplifying the equation:
300 kg * m/s = 200 kg * vf
vf = (300 kg * m/s) / 200 kg
vf = 1.5 m/s
Therefore, the final velocity of the two objects after the collision is 1.5 m/s.
To find the final velocity of the two objects after the collision, we can use the principle of conservation of momentum, which states that the total momentum of a system before a collision is equal to the total momentum after the collision.
The momentum of an object is given by the formula:
Momentum = Mass × Velocity
Let's denote the initial velocity of the 75 kg object as v1, and the initial velocity of the 125 kg object as v2. Both values are given in the problem:
v1 = 4 m/s (velocity of the 75 kg object)
v2 = 0 m/s (initially at rest)
Now, we can calculate the initial momentum of each object:
Initial momentum of the 75 kg object (m1): p1 = Mass × Velocity = 75 kg × 4 m/s = 300 kg·m/s
Initial momentum of the 125 kg object (m2): p2 = Mass × Velocity = 125 kg × 0 m/s = 0 kg·m/s
The total initial momentum before the collision is the sum of the individual momenta:
p_initial = p1 + p2 = 300 kg·m/s + 0 kg·m/s = 300 kg·m/s
Now, since the two objects stick together after the collision, they move with a common final velocity, which we'll denote as v_final. We can calculate the final momentum:
Final momentum = (mass1 + mass2) × v_final
Since the final momentum must be equal to the initial momentum (according to the conservation of momentum), we can set up the equation:
p_initial = (mass1 + mass2) × v_final
300 kg·m/s = (75 kg + 125 kg) × v_final
300 kg·m/s = 200 kg × v_final
Now, we can solve for the final velocity (v_final):
v_final = 300 kg·m/s / 200 kg = 1.5 m/s
Therefore, the final velocity of the two objects after the collision is 1.5 m/s.