Two objects move on a horizontal frictionless surface along the same line in the same direction which we shall refer to as foward direction. The trailing object of mass 2.0kg has a velocity of 15m/s foward. The leading object of mass 3.2 kg has avelocity of 11m/s foward. The trailing object catces up with the leading object and the two objects exprience a completely inelastic collision. what is the final velocity of the two objects

Question

Two objects move on a horizontal frictionless surface along the same line in the same direction which we shall refer to as foward direction. The trailing object of mass 2.0kg has a velocity of 15m/s foward. The leading object of mass 3.2 kg has avelocity of 11m/s foward. The trailing object catces up with the leading object and the two objects exprience a completely inelastic collision. what is the final velocity of the two objects

Answer 1

To find the final velocity of the two objects after the inelastic collision, we need to apply the principles of conservation of momentum.

Conservation of momentum states that the total momentum of a system remains constant before and after the collision, as long as no external forces are acting on the system. In this case, since the horizontal surface is frictionless, we can assume no external forces are present.

The momentum (p) of an object is defined as the product of its mass (m) and its velocity (v). Mathematically, it can be expressed as:

p = m * v

Before the collision, the trailing object has a momentum of:

p1 = m1 * v1 = 2.0 kg * 15 m/s = 30 kg*m/s

The leading object has a momentum of:

p2 = m2 * v2 = 3.2 kg * 11 m/s = 35.2 kg*m/s

Since the trailing object catches up with the leading object and the two objects experience a completely inelastic collision, they stick together after the collision and move as a single object.

Let the final combined mass of the two objects be "m" and the final velocity of the combined object be "v_f".

After the collision, the momentum of the combined object is:

p_f = m * v_f

According to the conservation of momentum, the total momentum before the collision (p1 + p2) is equal to the total momentum after the collision (p_f):

p1 + p2 = p_f

Substituting the respective momentum values:

30 kg*m/s + 35.2 kg*m/s = m * v_f

65.2 kg*m/s = m * v_f

To find the final velocity (v_f), we need to know the final combined mass (m) of the two objects.

To determine the final combined mass, we add the masses of the trailing and leading objects:

m = m1 + m2 = 2.0 kg + 3.2 kg = 5.2 kg

Returning to the momentum equation:

65.2 kg*m/s = (5.2 kg) * v_f

Simplifying the equation:

v_f = 65.2 kg*m/s / 5.2 kg

v_f ≈ 12.54 m/s

So, the final velocity of the two objects after the completely inelastic collision is approximately 12.54 m/s in the forward direction.