Two objects, with masses 10kg and 6kg respectively, move in the same direction in the same straight line at velocities 8m/s and 4m/s repectively, when they collide. The objects remain in contact with each other after collision. Calculate the common velocity and the direction in which they move after the collision.
the direction remains the same, and v can be found by conserving momentum:
10(8) + 6(4) = (10+8)v
To calculate the common velocity and direction in which the objects move after the collision, we can apply the principle of conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. The principle of conservation of momentum states that the total momentum of a closed system remains constant before and after a collision.
Let's denote the masses of the two objects as m1 and m2, and their initial velocities as v1 and v2, respectively. After the collision, the two objects combine and move with a common velocity, which we'll represent as v.
Based on the given data:
m1 = 10 kg, v1 = 8 m/s
m2 = 6 kg, v2 = 4 m/s
To solve for the common velocity (v) after the collision, we can use the following equation:
(m1 * v1) + (m2 * v2) = (m1 + m2) * v
Substituting the given values:
(10 kg * 8 m/s) + (6 kg * 4 m/s) = (10 kg + 6 kg) * v
80 kg*m/s + 24 kg*m/s = 16 kg * v
104 kg*m/s = 16 kg * v
Dividing both sides by 16 kg:
v = 104 kg*m/s / 16 kg
v = 6.5 m/s
So, the common velocity of the two objects after the collision is 6.5 m/s.
To determine the direction, we can analyze the initial velocities of the objects. Since both objects are moving in the same direction, their velocities are already aligned. Therefore, they will continue to move in the same direction after the collision.
Hence, the two objects will move together with a common velocity of 6.5 m/s in the same direction they were previously moving.