A cord passes over a weightless and frictionless pulley. Masses of 200 g and 300 g are attached to the ends of the cord. Find the distance the masses will move during the 5th second after they are started from rest.
This is called an Atwood's machine and the acceleration rate is
a = [(M2 - M1)/(M1 + M2)]*g
M2 (the 300 g mass) goes down while M1 (200 g)goes up at this acceleration rate.
a = g/5
Distance moved t seconds after starting = (a/2) t^2
Distance moved from t= 4 to t=5 seconds is:
= (a/2)(5^2 - 4^2)
= (g/10)(25 - 16)
= 8.82 m
thanks man!
Why did the masses start from rest? Because they wanted to make sure they were taking things slow and steady. As for the distance they will move during the 5th second, well, did you know that masses are actually quite shy? They like to keep their distances, so they'll try to avoid moving too much. But let me do the math and get back to you with a more serious answer. Stay tuned, my friend!
To find the distance the masses will move during the 5th second, we need to calculate the acceleration of the system first.
Given that the masses are attached by a cord passing over a weightless and frictionless pulley, we know that the tension in the cord will be the same on both sides of the pulley. Let's assume this tension as T.
Now, we can apply Newton's second law of motion to both masses separately:
For the 200 g mass:
Net force = Mass * Acceleration
T - T = (0.2 kg) * a
0 = (0.2 kg) * a
For the 300 g mass:
Net force = Mass * Acceleration
T - T = (0.3 kg) * a
0 = (0.3 kg) * a
Since both expressions are equal to zero, it means that the acceleration of the system is zero. This implies that the masses will not move during the 5th second.
To find the distance the masses will move during the 5th second, we need to determine the acceleration of the system first.
Since the cord is passing over a weightless and frictionless pulley, we can assume that the tension in the cord is the same on each side. Let's denote this tension as T.
The net force acting on the system is the difference between the two masses: 300g - 200g = 100g = 0.1 kg.
Using Newton's second law, F = ma, we can calculate the acceleration of the system:
F = ma
T - T = ma
0.1a = 0
a = 0 m/s^2
Since the acceleration is 0 m/s^2, the masses will not move during the 5th second.
Therefore, the distance the masses will move during the 5th second is 0 meters.