A body of mass 6kg moving at 8m/s collides with a stationary body of mass 10kg and sticks to it. Find the speed of the composite body immediately after the impact.
To find the speed of the composite body immediately after the impact, we can use the law of conservation of momentum. According to this law, the total momentum before the impact is equal to the total momentum after the impact.
The momentum (p) of an object is defined as the product of its mass (m) and its velocity (v): p = m * v.
Before the collision:
- The momentum of the first body is given by: p1 = m1 * v1, where m1 = 6 kg and v1 = 8 m/s.
- The momentum of the second body is zero since it's stationary: p2 = m2 * v2, where m2 = 10 kg and v2 = 0 m/s.
The total momentum before the collision is: p_total_before = p1 + p2.
After the collision, the two bodies stick together and move as a single composite body. Let's assume the velocity of the composite body is v_final.
After the collision:
- The mass of the composite body is the sum of the individual masses: m_final = m1 + m2 = 6 kg + 10 kg = 16 kg.
According to the law of conservation of momentum, the total momentum after the collision is p_total_after = m_final * v_final.
Since the total momentum before the collision is equal to the total momentum after the collision, we have:
p_total_before = p_total_after
Substituting the values, we get:
m1 * v1 + m2 * v2 = m_final * v_final
6 kg * 8 m/s + 10 kg * 0 m/s = 16 kg * v_final
48 kg·m/s = 16 kg * v_final
Now, we can solve for v_final:
v_final = 48 kg·m/s / 16 kg
v_final = 3 m/s
So, the speed of the composite body immediately after the impact is 3 m/s.
To find the speed of the composite body immediately after the impact, we can use the principles of conservation of momentum.
Momentum is defined as the product of mass and velocity: momentum = mass x velocity.
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. In other words, the sum of the momenta of the individual objects remains the same.
Before the collision:
The momentum of the first object (6kg) is given by: momentum1 = mass1 x velocity1 = 6 kg x 8 m/s = 48 kg•m/s.
The momentum of the second object (10kg) is zero since it is stationary: momentum2 = mass2 x velocity2 = 10 kg x 0 m/s = 0 kg•m/s.
After the collision:
The two objects stick together and become one composite body, so we can calculate the composite mass by adding the masses of the individual objects: mass_composite = mass1 + mass2 = 6 kg + 10 kg = 16 kg.
Let's assume the velocity of the composite body after the collision is v.
Using the principle of conservation of momentum, we can write:
momentum1_before_collision + momentum2_before_collision = momentum_composite_after_collision
This equation can be written as:
(mass1 x velocity1) + (mass2 x velocity2) = mass_composite x v
Substituting the values we have:
(6 kg x 8 m/s) + (10 kg x 0 m/s) = 16 kg x v
48 kg•m/s = 16 kg x v
Dividing both sides of the equation by 16 kg:
v = 48 kg•m/s ÷ 16 kg
v = 3 m/s
Therefore, the speed of the composite body immediately after the impact is 3 m/s.
momentum (speed*mass) is preserved. So,
8*6 = s(6+10)
s = 3