A 8 kg ball of clay moving at 3 m/s slams into a 2 kg ball of clay which is at rest. If two balls stuck together after collision what is the speed of the combined ball
conserve momentum.
8*3 + 2*0 = (8+2)v
To calculate the speed of the combined ball after the collision, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). Mathematically, p = m * v.
Let's denote the mass and velocity of the 8 kg ball as m1 and v1 respectively, and the mass and velocity of the 2 kg ball as m2 and v2 respectively.
Given:
m1 = 8 kg
v1 = 3 m/s
m2 = 2 kg
v2 = 0 m/s (as the second ball is at rest)
The total momentum before the collision is therefore:
p1 = m1 * v1
= 8 kg * 3 m/s
= 24 kg m/s
The total momentum after the collision is the sum of the individual momenta of the combined ball.
Let's denote the mass and velocity of the combined ball as M and V respectively.
Since the two balls stick together after the collision and move as one object, the mass of the combined ball is the sum of the masses of the two balls:
M = m1 + m2
= 8 kg + 2 kg
= 10 kg
To find the velocity of the combined ball, we can use the equation for momentum again:
p2 = M * V
= 10 kg * V
According to the law of conservation of momentum, the total momentum before the collision (p1 = 24 kg m/s) is equal to the total momentum after the collision (p2):
p1 = p2
=> 24 kg m/s = 10 kg * V
Now we can solve for V to find the velocity of the combined ball:
V = 24 kg m/s / 10 kg
≈ 2.4 m/s
Therefore, the speed of the combined ball after the collision is approximately 2.4 m/s.
To find the speed of the combined ball after the collision, we can apply the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision, provided no external forces are acting on the system.
The momentum of an object is calculated by multiplying its mass by its velocity. Therefore, we can calculate the initial momentum of the 8 kg ball of clay by multiplying its mass (m1 = 8 kg) by its initial velocity (v1 = 3 m/s):
Initial momentum of 8 kg ball = m1 * v1
Next, we need to calculate the initial momentum of the 2 kg ball, which is at rest. Since the ball is not moving, its initial velocity (v2) is zero. Thus, the initial momentum of the 2 kg ball (m2 = 2 kg) is:
Initial momentum of 2 kg ball = m2 * v2 = 2 kg * 0 m/s = 0 kg*m/s
Now, let's denote the final velocity of the combined ball as vf. Since the two clay balls stick together, their masses combine (m1 + m2) to form a single mass. Thus, the final momentum of the combined ball is:
Final momentum of combined ball = (m1 + m2) * vf
According to the law of conservation of momentum, the initial momentum should be equal to the final momentum. Therefore, we can equate the two expressions:
m1 * v1 + m2 * v2 = (m1 + m2) * vf
Substituting the given values:
8 kg * 3 m/s + 2 kg * 0 m/s = (8 kg + 2 kg) * vf
24 kg*m/s = 10 kg * vf
Dividing both sides of the equation by 10 kg:
vf = 24 kg*m/s / 10 kg = 2.4 m/s
Therefore, the speed of the combined ball after the collision is 2.4 m/s.