Two identical gliders slide toward each other on an air track. One moves at 2 m/s and the other at 1 m/s. If they stick together, the combination slides at ____________________.
A) 0.5 m/s.
B) 1 m/s.
C) 1.5 m/s
D) 2 m/s
E) 2.5 m/s.
To find the speed at which the combination slides, 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.
The formula for momentum is given by:
Momentum = mass × velocity
Since the gliders are identical, we can assume that they have the same mass. Therefore, the total momentum before the collision is equal to the sum of the individual momenta.
The momentum of the first glider (moving at 2 m/s) is:
Momentum of glider 1 = mass × velocity = m × 2 = 2m
The momentum of the second glider (moving at 1 m/s) is:
Momentum of glider 2 = mass × velocity = m × 1 = m
The total momentum before the collision is:
Total momentum before collision = Momentum of glider 1 + Momentum of glider 2
= 2m + m
= 3m
Now, after the collision, the two gliders stick together. We assume that the combined mass is 2m (the sum of the individual masses).
Therefore, the momentum of the combined gliders after the collision is:
Momentum of combined gliders = mass × velocity = (2m) × v
According to the law of conservation of momentum:
Total momentum before collision = Total momentum after collision
3m = (2m) × v
Now, we solve for v:
v = 3m / (2m)
v = 3/2
v = 1.5 m/s
Therefore, the combination of gliders slides at a speed of 1.5 m/s.
The answer is C) 1.5 m/s.
To find the velocity of the combination after the gliders stick together, 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.
The momentum of an object can be calculated by multiplying its mass by its velocity. Since the gliders are identical, they have the same mass. Let's assume their mass is 'm'.
Momentum of the first glider (before the collision) = mass * velocity = m * 2 m/s
Momentum of the second glider (before the collision) = mass * velocity = m * 1 m/s
Total momentum before the collision = m * 2 m/s + m * 1 m/s = 3m m/s
After the gliders stick together, they become a single object with the combined mass of the two gliders, which is 2m.
We can now calculate the velocity of the combined object by dividing the total momentum after the collision by the combined mass.
Velocity of the combination = Total momentum after the collision / Combined mass
= 3m m/s / 2m
= 3/2 m/s
Therefore, the combination slides at a velocity of 1.5 m/s. The correct answer is option C) 1.5 m/s.