mass 0.3kg is moving on the ground at speed 4m/s towards ball B which is at rest on the ground and has mass of 0.8kg. When A collides with B the ball remains in contact for 0.2 sec after the collision B moves forward with a velocity of 1.8m/s find the average force of A and B during collision and explain above the total kinetic energy of the system before and after the collision.
Initial momentum of A = .3*4 = 1.2 kg m/s
Final momentum of B = .8*1.8 = 1.44 kg m/s
change of momentum of B = 1.44-0 = 1.44
so
Force on B = change in momentum/time
= 1.44 kg m/s / .2 s = 7.2 Newtons
Now final velocity of A from conservation of momentum
1.2 = 1.44 + .3 Va
so
Va = - 0.8 m/s
so now the energy stuff
initial Ke = (1/2)(0.3)(16)
Final Ke = (1/2)(.3)(-.8)^2 + (1/2)(.8)(1.8)^2
I hope the final is less than the initial
To find the average force exerted during the collision and understand the change in kinetic energy, we can apply the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum:
The total momentum before the collision is equal to the total momentum after the collision.
Before the collision:
Momentum of object A (mA) = Mass of A * Velocity of A = 0.3 kg * 4 m/s = 1.2 kg m/s (to the right)
Momentum of object B (mB) = Mass of B * Velocity of B = 0.8 kg * 0 m/s = 0 kg m/s (as B is at rest)
Total momentum before the collision = mA + mB = 1.2 kg m/s (to the right)
After the collision:
The two objects stay in contact for 0.2 seconds, during which object B acquires a velocity of 1.8 m/s.
Momentum of object A after the collision = Mass of A * Final Velocity of A
Momentum of object B after the collision = Mass of B * Final Velocity of B
Since both A and B move together after the collision, their final velocities are the same.
Momentum of A after the collision = (0.3 kg)(Final Velocity of A)
Momentum of B after the collision = (0.8 kg)(Final Velocity of A)
Total momentum after the collision = Momentum of A after the collision + Momentum of B after the collision
Given that B moves forward with a velocity of 1.8 m/s after the collision, we have:
1.2 kg m/s = (0.3 kg)(Final Velocity of A) + (0.8 kg)(1.8 m/s) [Substituting the given values]
From this equation, we can calculate the velocity of A after the collision.
2. Conservation of kinetic energy:
The total kinetic energy before the collision is equal to the total kinetic energy after the collision, assuming no external forces.
Before the collision:
Kinetic energy of object A = (1/2) * Mass of A * (Velocity of A)^2
Kinetic energy of object B = (1/2) * Mass of B * (Velocity of B)^2
Total kinetic energy before the collision = Kinetic energy of A + Kinetic energy of B
After the collision:
Total kinetic energy after the collision = (1/2) * Total mass of A and B * (Final Velocity of A)^2
Note that while the velocity of B after the collision is given (1.8 m/s), we still need to calculate the final velocity of A.
To find the average force during the collision, we need to know the collision time or the distance over which the collision occurs. Unfortunately, that information is not provided in the question, which makes it impossible to calculate the average force during the collision.