Question

june 2010
5.
which body is in equilibrium?
(1) a satellite moving around earth in a circular
orbit
a cart rolling down a frictionless incline
an apple falling freely toward the surface of
earth
a block sliding at constant velocity across a
tabletop

Explanation:

Step1: Recall the condition for equilibrium

A body is in equilibrium when the net force acting on it is zero. According to Newton's second law \(F = ma\), if \(F_{net}=0\), then \(a = 0\) (where \(a\) is the acceleration).

Step2: Analyze each option

• Option 1: Satellite moving around Earth in a circular orbit

The satellite has a centripetal acceleration \(a=\frac{v^{2}}{r}\) (where \(v\) is the orbital - speed and \(r\) is the radius of the orbit). Since \(a
eq0\), the net force (centripetal force \(F = \frac{mv^{2}}{r}\)) is not zero. So, it is not in equilibrium.

• Option 2: Cart rolling down a frictionless incline

The acceleration of a cart on a frictionless incline is \(a = g\sin\theta\) (where \(g\) is the acceleration due to gravity and \(\theta\) is the angle of the incline). Since \(a
eq0\), from \(F = ma\), \(F_{net}
eq0\). So, it is not in equilibrium.

• Option 3: Apple falling freely

The acceleration of a freely - falling apple is \(a = g\) (where \(g\approx9.8\ m/s^{2}\)). Using \(F = ma\), \(F_{net}=mg
eq0\). So, it is not in equilibrium.

• Option 4: Block sliding at constant velocity

If the velocity \(v\) is constant, then the acceleration \(a=\frac{\Delta v}{\Delta t}=0\). From \(F = ma\), \(F_{net}=0\). So, the block is in equilibrium.

Answer:

D. a block sliding at constant velocity across a tabletop