An Atwood machine consists of two masses (m1 = 175 grams, m2 = 485 grams) connected by a string over a frictionless pulley. The initial height above the floor is 157 cm. Both masses start from rest at point A ; point B is just as m2 hits the floor.
What is the kinetic energy of the system at point B?
What is the velocity of the system at point B?
To determine the kinetic energy of the system at point B, we need to consider the change in potential energy and the work done to calculate the velocity of the system at point B.
1. Start by calculating the change in potential energy:
The potential energy of an object is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
For m1: PE1 = (0.175 kg) * (9.8 m/s^2) * (1.57 m)
For m2: PE2 = (0.485 kg) * (9.8 m/s^2) * (1.57 m)
Note: We convert the masses from grams to kilograms by dividing by 1000 to maintain consistent units.
The total change in potential energy is given by ∆PE = PE2 - PE1.
2. Calculate the work done:
The work done on the system is equal to the change in potential energy, as the system is frictionless. So the work done is W = ∆PE.
3. Using the work-energy principle:
The work done on the system is equal to the change in kinetic energy. Thus, W = ∆KE.
Therefore, ∆KE = W.
4. Calculate the kinetic energy at point B:
To calculate the kinetic energy at point B, we need to find the velocity of the system at that point. We can use the relationship between work and kinetic energy given by the formula KE = 0.5 * m * v^2, where m is the total mass of the system and v is the velocity.
Since the system consists of both masses m1 and m2, the total mass is m = m1 + m2.
Substitute the values of ∆KE and m into the equation KE = 0.5 * m * v^2 and solve for KE.
5. Calculate the velocity at point B:
Using the equation ∆KE = 0.5 * m * v^2, we can solve for v by substituting the values of ∆KE and m.
Rearrange the equation to solve for v: v = sqrt(2 * ∆KE / m).
Substitute the values of ∆KE and m into the equation to calculate v.
By following these steps, you should be able to calculate the kinetic energy of the system at point B and the velocity of the system at point B.