Question

4. The mass of ball A is 10 kilograms and the mass of ball B is 5 kilograms. If

Answer 1

(4) It is given that :

Mass of ball A, $m_A=10\ kg$

Mass of ball B, $m_B=5\ kg$

Initial velocity of ball A, $u_A=-3\ m/s$

Initial velocity of ball B, $u_B=3\ m/s$

Final velocity of ball A, $v_A=2m/s$

We have to find the final velocity of ball B after collision.

Since, it is a elastic collision. So the momentum remains conserved.

i.e.

$m_Au_A+m_Bu_B=m_Av_A+m_Bv_B$

$10\ kg\times (-3\ m/s)+5\ kg\times3\ m/s=10\ kg\times 2\ m/s+5\ kg\timesv_B$

$-30+15-20=5v_B$

$-35\ m/s=5v_B$

$-7\ m/s=v_B$

So, after collision the ball B moves from right to left with a speed of 7 m/s.

(5) In this part, the mass of each ball is same and velocity of ball A is twice of that of ball B such that

$u_A=2u_B$

$m_A=m_B=m$

If the collision of two balls is elastic, then using the conservation of momentum as

$3u_B=v_A+v_B$

This implies that the final velocities would be different.

If the collision is inelastic,

$3v_b=2mv_f$

$v_f=\dfrac{3v_b}{2}$

So, if there is inelastic collision the balls will move with a common velocities.

Answer 2

4.) We are told that ball A is travelling from right to left, which we will refer to as a positive direction, making the initial velocity of ball A, +3 m/s. If ball B is travelling in the opposite direction to A, it will be travelling at -3 m/s. The final velocity of A is +2 m/s. Using the elastic collision equation, which uses the conservation of linear momentum, we can solve for the final velocity of B.

MaVai + MbVbi = MaVaf + MbVbf

Ma = 10 kg and Mb = 5 kg are the masses of balls A and B.
Vai = +3 m/s and Vbi = -3 m/s are the initial velocities.
Vaf = +2 m/s and Vbf = ? are the final velocities.

(10)(3) + (5)(-3) = (10)(2) + 5Vbf
30 - 15 = 20 + 5Vbf
15 = 20 + 5Vbf
-5 = 5 Vbf
Vbf = -1 m/s

The final velocity of ball B is -1 m/s.

5.) We are now told that Ma = Mb, but Vai = 2Vbi

We can use another formula to look at this mathematically.

Vaf = [(Ma - Mb)/(Ma + Mb)]Vai + [(2Mb/(Ma + Mb)]Vbi

Since Ma = Mb we can simplify this formula.

Vaf = [(0)/2Ma]Vai + [2Ma/2Ma]Vbi
Vaf = Vbi

Vbf = [(2Ma/(Ma + Mb)]Vai + [(Ma - Mb)/(Ma + Mb)]Vbi
Vbf = [2Mb/2Mb]Vai + [(0)/2Mb]Vbi
Vbf = Vai

Vaf = Vbi
Vbf = 2Vbi

If the initial velocity of A is twice the initial velocity of B, then the final velocity of A will be equal to the initial velocity of B.

If the initial velocity of A is twice the initial velocity of B, then the final velocity of B will be twice the initial velocity of B.