Two objects A and B are involved in a totally elastic collision The mass of A is 8.8 kg and the mass of B is 0.5 kg. The velocity of A is 4.5 m/s and the velocity of B is 0 m/s. If they collide elastically, what will be the final velocity of A in m/s?
You have to use two equations:
conservation of momentum
a*Va+b*Vb=aVa'+bVb'
solve for Va'
Va'=(a*Va+b*Vb-bVb')/a
Now put that expression for va' into the conservation of momentum
1/2 aVa^2+1/2bVb^2=1/2a Va'^2 +1/2 b Vb'^2
and then start solving for Vb'
A bit of algebra will be required. Then go back an solve for Va'
How exactly are you supposed to use the second equation to solve for Vb' if you don't know Va'^2?
m1=8.8 kg, v1=4.5 m/s
m2=0.5 kg, v2=0
u1=?
u1= (m1-m2)v1/)m1+m2),
u2=2m1v1/(m1+m2).
In the case of completely elastic collision, not only momentum is conserved but KE is also conserved. Considering these two principles, you get two equations from which you can find V1 and V2 in terms m1,m2 and U1.
To find the final velocity of object A after the elastic collision, we can use the principle of conservation of momentum and kinetic energy.
1. First, let's calculate the initial momentum of object A (Pa) and object B (Pb) separately.
Momentum (P) = mass (m) * velocity (v)
For object A:
Pa = 8.8 kg * 4.5 m/s
For object B:
Pb = 0.5 kg * 0 m/s
Since the initial velocity of object B is 0 m/s, its initial momentum is also 0.
2. Next, let's calculate the total initial momentum (Pi) of the system.
Pi = Pa + Pb
Since Pb is 0, the total initial momentum is equal to Pa.
3. According to the conservation of momentum, the total momentum before the collision (Pi) is equal to the total momentum after the collision (Pf).
Pf = Pi
4. After the collision, object B starts moving with a final velocity (vbf), and object A continues moving with a final velocity (vaf). Since it is an elastic collision, both objects will still be moving.
Pf = ma * vaf + mb * vbf
Where:
ma = mass of object A
vaf = final velocity of object A
mb = mass of object B
vbf = final velocity of object B
5. Substituting the given values into the equation, we can solve for vaf.
Pa = ma * vaf + mb * vbf
8.8 kg * 4.5 m/s = 8.8 kg * vaf + 0.5 kg * vbf
Since the collision is elastic, the final velocity of object B can be found using the equation:
pb * vbf = 0.5 * vbf = -8.8 * (vaf - 4.5)
0.5 * vbf = -8.8 * vaf + 39.6
vbf = -17.6 * vaf + 79.2 ----- (1)
Substituting this equation (1) back into the original momentum equation:
8.8 * 4.5 = 8.8 * vaf + 0.5 * (-17.6 * vaf + 79.2)
Simplifying the equation:
39.6 = (8.8 - 8.8 * 17.6) * vaf + 0.5 * 79.2
39.6 = (8.8 - 154.88) * vaf + 39.6
By canceling like terms:
0 = -146.08 * vaf
Therefore, vaf (final velocity of object A) will be 0, as there has been no change in its velocity after the collision.
So, the final velocity of object A after the elastic collision will be 0 m/s.