Physlet Physics by Christian and Belloni: Problem 4.11 compadre.org Open the simulation, a Modified Atwood's Machine.

Mathematician George Atwood invented it, in 1784 to show the physics of Newton's 2^nd Law.We analyze it now (2021).

Click run, and watch how the two masses move.Gravity pulls down on the hanging weight, it accelerates down, and pulls the mass on the lab track to the rightthey're connected by a string going over a pulley.No friction.

1. Our data indicates an initial speed of zero and a final speed of v = ______ m/s (click on half-red dot at end of v_x vs t graph,

a yellow box pops up, and the speed is the second number in the yellow box).The time interval is .8 s.Calculate acceleration from v = v₀ + a t, a = ______ m/s² (both blanks to nearest hundredth).

This "a" is about 1/3 of g = 9.8 m/s². Explanation: first call their masses m_A (mass on horizontal lab track) and m_B (hanging mass).

The masses are connected by a string, and gravity only pulls down on m_B.It is this force that accelerates both, due to the string.Gravity only acts on m_B, while accelerating both.The presence of m_A retards and slows the acceleration, from 9.8 m/s².

We will analyze this using F = m a, for both masses separately; the 2^nd Law equation is used because both masses accelerate.

The lecture stated that "F" is the force casing the acceleration, So this is F = F_w = m_B g, meaning the hanging mass's weight causes the acceleration.

The "m" in F = m a, is the total mass that accelerates.Both do, so m = m_A + m_B.

Thus, F = m a becomes F_w = m_B g = (m_A + m_B) a.

The lecture solved for "a", a = m_B g / (m_A + m_B)