A body B moving with a velocity of 20m/s collides with another body A, moving in the same direction on same horizontal line, with a velocity of 10m/s. If the mass of a body A is three times the mass of a body B, and the
collision is perfectly elastic.
calculate the velocities of A and B after collision and calculate the impulse on A and B
I want the answer
M1 = 3M, V1 = 20 m/s.
M2 = M, V2 = 10 m/s.
M1*V1 + M2*V2 = M1*V3+M2*V4.
3M*20+M*10 = 3M*V3+M*V4.
Divide both sides by M:
60+10 = 3V3+V4,
Eq1: 3V3+V4 = 70.
V3 = ((M1-M2)V1 + 2M2*V2)/(M1+M2).
V3 = (2M*20 + 2M*10)/4M = 60M/4M = 15 m/s. = Velocity of M1(B).
In Eq1, replace V3 with 15 and solve for V4.
calculate A and B after the collision
in 2021
I want answer
calculate A and B after the collision
To calculate the velocities of bodies A and B after the collision and the impulse on A and B, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum:
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:
(mass_A * velocity_A_initial) + (mass_B * velocity_B_initial) = (mass_A * velocity_A_final) + (mass_B * velocity_B_final)
In this case, we have the following values:
mass_A = 3 * mass_B
velocity_A_initial = 10 m/s
velocity_B_initial = 20 m/s
Substituting these values into the equation, we'll have:
(3 * mass_B * 10) + (mass_B * 20) = (3 * mass_B * velocity_A_final) + (mass_B * velocity_B_final)
Simplifying the equation, we get:
30 * mass_B + 20 * mass_B = 3 * mass_B * velocity_A_final + mass_B * velocity_B_final
2. 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. Mathematically, this can be expressed as:
0.5 * mass_A * (velocity_A_initial)^2 + 0.5 * mass_B * (velocity_B_initial)^2 = 0.5 * mass_A * (velocity_A_final)^2 + 0.5 * mass_B * (velocity_B_final)^2
Now, let's solve the equations to find the velocities and impulse:
1. Solve for velocities A_final and B_final:
Using both equations, we can solve for the unknown velocities by dividing the first equation by mass_B:
30 + 20 = 3 * velocity_A_final + velocity_B_final
Then, substitute (3 * mass_B) with mass_A (from the given information):
50 = 3 * velocity_A_final + velocity_B_final
2. Solve for impulse on A and B:
The impulse on an object can be calculated by multiplying the change in velocity with the object's mass. So, to calculate the impulse on bodies A and B, we'll use the following formulas:
Impulse_A = mass_A * (velocity_A_final - velocity_A_initial)
Impulse_B = mass_B * (velocity_B_final - velocity_B_initial)
Substitute the known values into the formulas, including the velocities calculated in the previous step.
I hope this helps you understand how to calculate the velocities and impulse in this collision scenario!