A mass of 5kg decending vertically draws up a mass of 3kg by means of a light string passing over a pulley. At the end of 4s the string breaks. how much higher the 3kg mass would go?
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To determine how much higher the 3kg mass would go after the string breaks, we need to understand the principles of conservation of energy and the relationship between gravitational potential energy and kinetic energy.
First, let's calculate the potential energy of the system before the string breaks. The potential energy of an object at a certain height is given by the equation:
Potential Energy = Mass * Gravity * Height
For the 5kg mass, the potential energy at the initial height is:
Potential Energy (5kg) = 5kg * 9.8m/s^2 * H1
Now, since the string is passing over a pulley, the potential energy of the 3kg mass is also defined by the same equation:
Potential Energy (3kg) = 3kg * 9.8m/s^2 * H2
Since the masses are connected by a light string, the distance traveled by the 5kg mass would be equal to the distance traveled by the 3kg mass:
H1 = H2
Therefore, the potential energy of the 5kg mass is equal to the potential energy of the 3kg mass:
5kg * 9.8m/s^2 * H1 = 3kg * 9.8m/s^2 * H2
Now, let's consider the time it takes for the string to break. We are given that this occurs after 4 seconds. During this time, both masses are accelerating due to gravity. The 5kg mass is accelerating downward while the 3kg mass is accelerating upward.
Using the equation for vertical motion:
Final Velocity = Initial Velocity + (Acceleration * Time)
For the 5kg mass:
Final Velocity (5kg) = 9.8m/s^2 * 4s
For the 3kg mass:
Final Velocity (3kg) = -9.8m/s^2 * 4s (negative sign indicates upward direction)
Now, we can calculate the height that each mass reaches after the string breaks.
For the 5kg mass:
Height (5kg) = Initial Velocity (5kg) * Time + (1/2) * Acceleration * Time^2
For the 3kg mass:
Height (3kg) = Initial Velocity (3kg) * Time + (1/2) * Acceleration * Time^2
Since the initial velocities of both masses are zero:
Height (5kg) = (1/2) * Acceleration (5kg) * Time^2
Height (3kg) = (1/2) * Acceleration (3kg) * Time^2
Now, we can plug in the values:
Height (5kg) = (1/2) * 9.8m/s^2 * (4s)^2
Height (3kg) = (1/2) * -9.8m/s^2 * (4s)^2
This will give us the heights reached by each mass after 4 seconds. The difference between these heights will tell us how much higher the 3kg mass would go after the string breaks.