a ball of putty has a mass of 1.5kg and is rolling toward the north with a velocity of 2m/s. it collides with another putty ball with the same mass travelling towards the east with a velocity of 10m/s. find the velocity of the combined mass after a completely inelastic collision
momentum is conserved
the mass is doubled, so the velocity components are halved
... 1 m/s N and 5 m/s E
magnitude of v ... v^2 = 1^2 + 5^2
direction ... tan(Θ) = 1 / 5
... Θ is the angle north of east
Given:
M1 = 1.5kg, V1 = 2 m/s[90o].
M2 = 1.5kg, V2 = 10 m/s[0o].
V3 = Velocity of M1 and M2 after collision.
Momentum before = Momentum after.
M1*V1 + M2*V2 = M1*V3 + M2*V3.
1.5*2i + 1.5*10 = 1.5V3 + 1.5V3,
15 + 3i = 3V3,
V3 = 5 + 1i = 5.1m/s[11.3o].
To find the velocity of the combined mass after a completely inelastic collision, we can use the principles of conservation of momentum.
The momentum of an object is defined as the product of its mass and velocity. In this case, we have two putty balls colliding with each other. Let's call the velocity of the first putty ball rolling towards the north "v1" and the velocity of the second putty ball moving towards the east "v2". The mass of both balls is 1.5 kg.
Before the collision, we need to calculate the momentum of each ball separately.
Momentum of the first ball (p1) = mass of first ball (m1) * velocity of first ball (v1)
= 1.5 kg * 2 m/s
= 3 kg·m/s
Momentum of the second ball (p2) = mass of the second ball (m2) * velocity of second ball (v2)
= 1.5 kg * 10 m/s
= 15 kg·m/s
Now, let's consider the collision where the two putty balls stick together and move as one combined mass after the collision.
The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
Total initial momentum = Total final momentum
(p1 + p2) = Total momentum after the collision
Substituting the values of p1 and p2:
(3 kg·m/s + 15 kg·m/s) = Total momentum after the collision
18 kg·m/s = Total momentum after the collision
Now, since the two balls stick together, they move as one combined mass. Let's call the velocity of the combined mass after the collision "v_final".
The total momentum after the collision is given by:
Total momentum after the collision = combined mass * v_final
Since the mass of both balls is 1.5 kg, the combined mass is 1.5 kg + 1.5 kg = 3 kg.
Substituting the values into the equation:
18 kg·m/s = 3 kg * v_final
Simplifying the equation:
v_final = 18 kg·m/s / 3 kg
v_final = 6 m/s
Therefore, the velocity of the combined mass after the completely inelastic collision is 6 m/s.