Applying Newton’s Laws: Equilibrium, Connected Systems, and Variable Forces

All flashcards

What does a free-body diagram represent?

A chosen system and all external forces acting on it.

What distinguishes static from dynamic equilibrium?

Static equilibrium is rest; dynamic equilibrium is motion at constant velocity.

What acceleration constraint applies to objects connected by an ideal string?

They have equal acceleration magnitudes along the string.

What does a scale measure for a person standing on it?

The magnitude of the normal force exerted by the scale.

How can acceleration depending on speed be related to displacement?

Use the chain-rule relation $a\,ds=v\,dv$.

Quiz questions

1. Two objects are connected by a light, inextensible string over an ideal pulley. What is true of their accelerations?Answer: Their acceleration magnitudes along the string are equal.
2. A person of mass $m$ accelerates upward at $a$ in an elevator. What is the scale’s normal force on the person?Answer: $m(g+a)$
3. In an ideal Atwood machine, $m_2>m_1$. Which way do the masses accelerate?Answer: $m_2$ downward and $m_1$ upward.
4. A barge accelerates along the direction of an applied force while water drag acts opposite its motion. Which equation gives its net force along that direction?Answer: $F_{\text{app}}-F_D=ma$
5. For constant mass and a known time-dependent acceleration $a(t)$, how can velocity change over a time interval be found?Answer: Integrate $a(t)$ with respect to time over the interval.