16-g mass is moving in the +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 the collision.
16*30 - 4*50 = 20 v
From the - x direction, m1v1 =4*(-50) =-200gm/s
And from +x direction, m2v2=16 *30=480
Where M1V1 + M2V2=(M1 + M2)V.
=> - 200 + 480 =(4+16)v
V= 280/20 =14m/s.
To find the velocity of the masses after the collision, we can apply the principle of conservation of momentum.
The momentum before the collision can be calculated by multiplying the mass with the velocity:
Mass 1 momentum before collision = 16 g * 30 cm/s = 480 g·cm/s
Mass 2 momentum before collision = 4 g * (-50 cm/s) = -200 g·cm/s
Since momentum is conserved in a collision, the total momentum after the collision will be equal to the total momentum before the collision:
Total momentum before collision = Total momentum after collision
480 g·cm/s + (-200 g·cm/s) = Total momentum after collision
Simplifying the equation gives:
280 g·cm/s = Total momentum after collision
After the collision, the two masses stick together, becoming a single mass. Let's denote this combined mass as M:
Momentum of the combined mass after the collision = M * velocity after the collision
Since the two masses stick together, they will have the same velocity after the collision. Let's denote this velocity as V:
Momentum of the combined mass after the collision = M * V
Since momentum is conserved, we can set the two equations equal to each other:
280 g·cm/s = M * V
To find the velocity after the collision (V), we need to determine the combined mass (M). The combined mass is simply the sum of the two masses:
Combined mass (M) = 16 g + 4 g = 20 g
Substituting this value into the equation gives:
280 g·cm/s = 20 g * V
Simplifying the equation gives:
V = 280 g·cm/s / 20 g
Dividing both sides by g to convert from g·cm/s to cm/s gives:
V = 280 cm/s / 20
V = 14 cm/s
Therefore, the velocity of the masses after the collision is 14 cm/s in the direction of the positive x-axis.
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.
The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by the equation: p = m * v, where m is the mass and v is the velocity.
Let's denote the initial velocity of the 16-g mass as v1i (initial velocity of mass 1) and the initial velocity of the 4-g mass as v2i (initial velocity of mass 2). The final velocity of the combined masses after the collision will be denoted as vf.
According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Total initial momentum before the collision = Total final momentum after the collision
(m1 * v1i) + (m2 * v2i) = (m1 + m2) * vf
Substituting the given values:
(16 g * 30 cm/s) + (4 g * (-50 cm/s)) = (16 g + 4 g) * vf
Remember to convert grams to kilograms and centimeters to meters to have consistent units:
(0.016 kg * 0.3 m/s) + (0.004 kg * (-0.5 m/s)) = (0.016 kg + 0.004 kg) * vf
Now let's solve for vf:
(0.0048 kg m/s) + (-0.002 kg m/s) = (0.02 kg) * vf
(0.0028 kg m/s) = (0.02 kg) * vf
vf = (0.0028 kg m/s)/(0.02 kg)
vf = 0.14 m/s
Therefore, after the collision, the combined masses will move together in the +x direction at a velocity of 0.14 m/s.