Impulse/ Velocity

Question

Two objects travel towards each other and undergo a perfectly inelastic interaction. Before they collide, object A has a mass of 903g and a velocity of 16.8m/s, while object B has a mass of 333g and a velocity of 16.2m/s. The interaction takes 1s from start to finish.

Beware: if both initial velocities are positive (or negative), that is saying that they are travelling in the same direction (for positive numbers, both are going to the right), however because their speeds are different, they are technically still "travelling towards each other)! The point is, don't make one negative when you do the calculations unless it was negative as written here/above!

What is the impulse by A on B?    unit   

What is the force by A on B?    unit   

What is the impulse by B on A?    unit   

What is the force by B on A?    unit   

Answer 1

First, we need to use conservation of momentum to find the final velocity of the combined object after the collision. Since momentum is conserved in an inelastic collision, we have:

(mA * vA) + (mB * vB) = (mA + mB) * vf

where mA and vA are the mass and velocity of object A before the collision, mB and vB are the mass and velocity of object B before the collision, and vf is the velocity of the combined object after the collision.

Substituting the given values, we get:

(0.903 kg) * (16.8 m/s) + (0.333 kg) * (-16.2 m/s) = (0.903 kg + 0.333 kg) * vf

Solving for vf, we get:

vf = 1.52 m/s

(a) The impulse by A on B is equal to the change in momentum of B, which is:

Impulse = mB * (vf - vB)

Substituting the given values, we get:

Impulse = (0.333 kg) * (1.52 m/s - 16.2 m/s) = -4.88 Ns

Since impulse is a vector quantity, the negative sign indicates that the impulse by A on B is in the opposite direction to the initial velocity of B.

(b) The force by A on B can be found using the impulse-momentum theorem, which states that the impulse on an object is equal to the change in its momentum, and the change in momentum is equal to the force multiplied by the time interval over which the force acts:

Impulse = Force * time

Rearranging this equation, we get:

Force = Impulse / time

Substituting the given values, we get:

Force = (-4.88 Ns) / (1 s) = -4.88 N

The negative sign indicates that the force by A on B is in the opposite direction to the initial velocity of B.

(c) The impulse by B on A is equal to the change in momentum of A, which is:

Impulse = mA * (vf - vA)

Substituting the given values, we get:

Impulse = (0.903 kg) * (1.52 m/s - 16.8 m/s) = -13.4 Ns

Since impulse is a vector quantity, the negative sign indicates that the impulse by B on A is in the opposite direction to the initial velocity of A.

(d) The force by B on A can be found using the same method as in part (b):

Force = Impulse / time

Substituting the given values, we get:

Force = (-13.4 Ns) / (1 s) = -13.4 N

The negative sign indicates that the force by B on A is in the opposite direction to the initial velocity of A.