A 16-g mass is moving in +x direction at 30 cm/s while a 4-g mass is moving in the -x direction at 50 cm/s. they collide head-on and stick together. Find their velocity after collision?
x momentum = 16*30 = 480 g cm/s
-x momentum = 4*50 = -200 g cm/s
total x momentum = +280 g cm/s
That will NOT CHANGE !
new mass = 16 + 4 = 20 g
so
20 * Vx = 280
Vx = 14 cm/s
To find the velocity of the masses after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let's assign some variables for the given information:
- Mass 1 (m1) = 16 g = 0.016 kg
- Velocity 1 (v1) = +30 cm/s
- Mass 2 (m2) = 4 g = 0.004 kg
- Velocity 2 (v2) = -50 cm/s
The momentum (p) of an object is equal to the product of its mass (m) and velocity (v):
p = m * v
We can calculate the initial momentum (p_initial) of the two masses separately:
p_initial1 = m1 * v1
p_initial2 = m2 * v2
Next, we know that after the collision, both masses stick together, so they move with the same velocity (v_after). Therefore, their combined mass (m_combined) would be the sum of their individual masses:
m_combined = m1 + m2
Now, using the conservation of momentum, we can set up an equation equating the total momentum before and after the collision:
p_initial1 + p_initial2 = m_combined * v_after
Now let's substitute the given values into the equation and solve for v_after:
p_initial1 + p_initial2 = m_combined * v_after
(m1 * v1) + (m2 * v2) = (m1 + m2) * v_after
(0.016 kg * 30 cm/s) + (0.004 kg * -50 cm/s) = (0.016 kg + 0.004 kg) * v_after
(0.48 kg cm/s) + (-0.2 kg cm/s) = (0.02 kg) * v_after
0.28 kg cm/s = 0.02 kg * v_after
Now, divide both sides of the equation by 0.02 kg to solve for v_after:
v_after = (0.28 kg cm/s) / (0.02 kg)
v_after = 14 cm/s
Therefore, the velocity of the masses after the collision is 14 cm/s in the positive x-direction.
To find the velocity of the masses after the collision, we can use the principle of conservation of momentum.
The equation for conservation of momentum is:
(m1 * v1) + (m2 * v2) = (m1 + m2) * V
Where:
m1 is the mass of the first object (16 g)
v1 is the velocity of the first object (30 cm/s)
m2 is the mass of the second object (4 g)
v2 is the velocity of the second object (-50 cm/s)
V is the velocity of the combined mass after the collision.
Plugging in the given values into the equation, we have:
(16 g * 30 cm/s) + (4 g * -50 cm/s) = (16 g + 4 g) * V
Converting the masses from grams to kilograms (1 g = 0.001 kg):
(0.016 kg * 30 cm/s) + (0.004 kg * -50 cm/s) = (0.016 kg + 0.004 kg) * V
Converting the velocities from cm/s to m/s (1 m = 100 cm):
(0.016 kg * 0.3 m/s) + (0.004 kg * -0.5 m/s) = (0.02 kg) * V
Simplifying the equation:
0.0048 kg m/s + (-0.002 kg m/s) = 0.02 kg * V
0.0028 kg m/s = 0.02 kg * V
Dividing both sides by 0.02 kg:
0.0028 kg m/s / 0.02 kg = V
0.14 m/s = V
Therefore, the velocity of the masses after the collision is 0.14 m/s in the direction of the positive x-axis.