A Modified Atwood's machine (the pulley with two mass system used in class on in the Modified Atwood physlet) has a 10.0 N cart on a frictionless, horizontal track with a 10.0 N hanging weight attached to a string connecting the two weights. A second track is set up where the hanging weight is replaced by a person who can maintain a 10.0 N pull on the string (as measured with a force probe). Which set-up has the greater acceleration?
One is accelerating 20kg, one is accelerating 10 kg, right?
F=systemmass*a
To determine which setup has the greater acceleration, we need to consider Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
In the first setup, with the cart and the hanging weight, the net force acting on the system is the difference between the weight of the hanging weight (10.0 N) and the weight of the cart (10.0 N), which is zero. Since there is no net force, the system remains at rest or moves with a constant velocity, having an acceleration of zero.
In the second setup, with the person pulling the string, the net force acting on the system is the force exerted by the person (10.0 N). This net force is applied to the cart, which has a mass. Therefore, there is a non-zero net force acting on the system.
Since the net force is non-zero in the second setup, it will result in an acceleration. By Newton's second law, the magnitude of the acceleration is directly proportional to the net force and inversely proportional to the mass. As both setups have the same mass (assuming the person's mass is negligible compared to the cart and hanging weight), the setup with the person pulling the string will have a greater acceleration than the first setup.
Therefore, the second setup, with the person pulling the string, has the greater acceleration.