Ball A mass 0.5kg rolls at 3m/s into ball B which is stationary and has mass of 0.9kg if the collision brings ball A to rest what is the velocity of ball B immediately after the collision
conservation of momentum
.5(3)+0=0+.9 V
solve for V
To find the velocity of ball B immediately after the collision, we can use the principle of conservation of momentum.
The momentum of an object is defined as the mass of the object multiplied by its velocity. According to the conservation of momentum principle, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, the momentum of ball A is given by:
Momentum of A = mass of A * velocity of A
= 0.5 kg * 3 m/s
= 1.5 kg*m/s
Since ball B is stationary (velocity = 0 m/s), its momentum before the collision is:
Momentum of B = mass of B * velocity of B
= 0.9 kg * 0 m/s
= 0 kg*m/s
The total momentum before the collision is the sum of the individual momenta of the two balls:
Total momentum before = Momentum of A + Momentum of B
= 1.5 kg*m/s + 0 kg*m/s
= 1.5 kg*m/s
After the collision, ball A comes to rest, so its velocity is 0 m/s. The velocity of ball B after the collision can be represented as v.
Therefore, the momentum of ball A after the collision is:
Momentum of A' = mass of A * velocity of A'
= 0.5 kg * 0 m/s
= 0 kg*m/s
The momentum of ball B after the collision is:
Momentum of B' = mass of B * velocity of B'
= 0.9 kg * v
According to the conservation of momentum principle, the total momentum after the collision should be equal to the total momentum before the collision:
Total momentum after = Momentum of A' + Momentum of B'
= 0 kg*m/s + 0.9 kg * v
= 0.9 kg * v
Since the total momentum before (1.5 kg*m/s) is equal to the total momentum after (0.9 kg * v), we can equate the two expressions:
1.5 kg*m/s = 0.9 kg * v
Solving for v, we can rearrange the equation:
v = (1.5 kg*m/s) / 0.9 kg
v ≈ 1.67 m/s
Therefore, the velocity of ball B immediately after the collision is approximately 1.67 m/s.
To find the velocity of ball B immediately after the collision, we can use the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v). Mathematically, it can be expressed as:
p = m * v
Let's denote the initial velocity of ball A as v1, the final velocity of ball A as v1', and the final velocity of ball B as v2.
Since ball A comes to rest after the collision, we have v1' = 0 m/s.
The total momentum before the collision (p_initial) is the sum of the momentum of ball A and ball B, which can be calculated as:
p_initial = (m1 * v1) + (m2 * v2)
where
m1 = mass of ball A = 0.5 kg
v1 = initial velocity of ball A = 3 m/s
m2 = mass of ball B = 0.9 kg
Therefore,
p_initial = (0.5 kg * 3 m/s) + (0.9 kg * v2)
Since momentum is conserved, the total momentum after the collision (p_final) is equal to zero, as ball A comes to rest. Hence, we have:
p_final = 0
Using the conservation of momentum principle, we can equate the initial and final total momentum and solve for v2:
(0.5 kg * 3 m/s) + (0.9 kg * v2) = 0
Simplifying the equation, we get:
1.5 kg + 0.9 kg * v2 = 0
0.9 kg * v2 = -1.5 kg
v2 = -1.5 kg / 0.9 kg
v2 = -1.67 m/s
Therefore, the velocity of ball B immediately after the collision is approximately -1.67 m/s. The negative sign indicates that the ball B moves in the opposite direction to the initial motion of ball A.