An Atwood machine has two masses connected by a string over a pulley. The mass on one side is decreasing at a rate of 2 kg/s, while the other mass remains constant. Calculate the acceleration of the system.
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The acceleration of the system can be calculated using the following formula:
a = (m2 - m1) * g / (m1 + m2)
Where:
- a is the acceleration of the system
- m1 is the mass that is decreasing (in this case decreasing at a rate of 2 kg/s)
- m2 is the constant mass
- g is the acceleration due to gravity (approximately 9.8 m/s²)
Given that m1 is decreasing at a rate of 2 kg/s, we can assume that the change in m1 over time (dm1/dt) is -2 kg/s.
Plugging these values into the formula:
a = (-2 - 0) * 9.8 / (0 + 2)
a = -19.6 / 2
a = -9.8 m/s²
Therefore, the acceleration of the system is -9.8 m/s² (negative sign indicates that the direction of acceleration is downwards).
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