Atwood's Machine problem
The main purpose of the Atwood's machine problem is to develop a more complete comprehension of the application of Newton's 2nd Law.
The main idea is the recognition that the force required is the net force (because force is a vector => direction matters), and the mass required is the total mass (because mass is a scalar, and the masses move together).
Example:
| Suppose to objects are suspended from a frictionless pulley by a massless string. One mass is greater than the other. What is the acceleration of the masses? Let the mass on the left, m1 = 15.0 kg, and mass on the right, m2 = 25.0 kg. Then the weight pulling counter clockwise to the left is Fg1 = m1g = (15.0 kg)(9.81 m/s2) = 147 N The weight pulling clockwise to the right is Fg2 = m2g = (25.0 kg)(9.81 m/s2) = 245 N So the net force on the system, FNET = Fg1 - Fg2 = 245 N - 147 N = 98 N [The forces are subtracted because they are vectors acting in opposite directions.] The total mass of the system is mT = m1 + m2 = 25.0 kg + 15.0 kg = 40.0 kg [The masses are added because mass is a scalar.] And the acceleration of the system is a = FNET/mT = (98 N)/(40.0 kg) = 2.5 N/kg = (2.5 kg m/s2)/kg = 2.5 m/s2.
|
 |
