Two identical gliders slide toward each other on an air track. One moves at 1m/s and the other at 2m/s. they collide and stick. the combined mass moves at
A. 1.5m/s
B. 1/3m/s
C. 1/6m/s
D. 3/4m/s
E. 1/2m/s
which of this options is the right answer?
The option that preserves total momentum is the correct one.
Note that the final mass is 2M, and that the initial individual momenta have opposite signs.
(2m/s)*M -(1m/s)*M = 2M*Vfinal
Solve for Vfinal
To determine the velocity of the combined mass after the collision, we need to apply the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity. Since the gliders have identical masses, the total mass before the collision is the sum of their individual masses.
Before the collision:
Total momentum = (Mass of first glider x Velocity of first glider) + (Mass of second glider x Velocity of second glider)
After the collision, the two gliders stick together and move as a single combined mass. Let's call the mass of the combined gliders "M".
After the collision:
Total momentum = Mass of combined gliders x Velocity of combined gliders
Since momentum is conserved, we can equate the total momentum before the collision to the total momentum after the collision:
(Mass of first glider x Velocity of first glider) + (Mass of second glider x Velocity of second glider) = Mass of combined gliders x Velocity of combined gliders
Plugging in the given values:
(1kg x 1m/s) + (1kg x 2m/s) = M x Velocity of combined gliders
Simplifying:
1kg + 2kg = M x Velocity of combined gliders
3kg = M x Velocity of combined gliders
To find the velocity of the combined gliders, we need to solve for M x Velocity of combined gliders. We divide both sides of the equation by M:
(3kg / M) = Velocity of combined gliders
Now, we need to determine the value of M, the mass of the combined gliders. Since the gliders are identical, we can add their masses:
M = Mass of first glider + Mass of second glider
M = 1kg + 1kg
M = 2kg
Plugging in the value of M into the equation:
(3kg / 2kg) = Velocity of combined gliders
Simplifying:
(3/2) = Velocity of combined gliders
Therefore, the velocity of the combined mass after the collision is 3/2 m/s, which is equivalent to 1.5 m/s.
So the correct answer is A. 1.5m/s.