A 1.2 kg object moving at initial velocity 2.0m/s collides elastically with a stationary 0.5kg object horizontally. Calculate
A) the velocity of each object after the collision.
B) the impulsive force if the contact time is 0.3 s.
To calculate the velocities of the objects after the collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
A) Conservation of momentum:
In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.
Let's assume the initial velocity of the 0.5kg object (stationary) is 0 m/s. The initial momentum of the system can be calculated as:
Initial momentum = (mass1 x velocity1) + (mass2 x velocity2)
= (1.2 kg x 2.0 m/s) + (0.5 kg x 0 m/s)
= 2.4 kg·m/s
Now, let's assume the final velocities of the 1.2 kg object and the 0.5 kg object are v1 and v2, respectively. The final momentum of the system can be calculated as:
Final momentum = (mass1 x v1) + (mass2 x v2)
Applying conservation of momentum, we have:
Initial momentum = Final momentum
2.4 kg·m/s = (1.2 kg x v1) + (0.5 kg x v2) ---(Equation 1)
B) Conservation of kinetic energy:
In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
The initial kinetic energy of the system before the collision can be calculated as:
Initial kinetic energy = (1/2 x mass1 x (velocity1)^2) + (1/2 x mass2 x (velocity2)^2)
= (1/2 x 1.2 kg x (2.0 m/s)^2) + (1/2 x 0.5 kg x (0 m/s)^2)
= 2.4 J
Similarly, the final kinetic energy of the system after the collision can be calculated as:
Final kinetic energy = (1/2 x mass1 x (v1)^2) + (1/2 x mass2 x (v2)^2)
Applying conservation of kinetic energy, we have:
Initial kinetic energy = Final kinetic energy
2.4 J = (1/2 x 1.2 kg x (v1)^2) + (1/2 x 0.5 kg x (v2)^2) ---(Equation 2)
Now, we have two equations (Equation 1 and Equation 2) with two unknowns (v1 and v2). We can solve these equations simultaneously to find the values of v1 and v2.
Solving these equations, we get:
v1 = -1.2 m/s
v2 = 4.8 m/s
Therefore, after the collision:
- The 1.2 kg object moves in the opposite direction with a velocity of 1.2 m/s.
- The 0.5 kg object moves to the right with a velocity of 4.8 m/s.
B) To calculate the impulsive force, we can use the formula:
Impulsive force = Change in momentum / Contact time
We already know the initial and final velocities of the 1.2 kg object (from above). The change in momentum of the 1.2 kg object can be calculated as:
Change in momentum = mass x (final velocity - initial velocity)
= 1.2 kg x (1.2 m/s - 2.0 m/s)
= -0.96 kg·m/s
Now, plugging in the values, we can calculate the impulsive force:
Impulsive force = (-0.96 kg·m/s) / (0.3 s)
= -3.2 N
Therefore, the impulsive force exerted during the collision is -3.2 N (negative sign indicates the force is in the opposite direction of the motion).