Question

consider the force diagrams below for five different situations. think! there may be more than one answer!

which of the object(s) above could be moving to the right at a constant speed?

Explanation:

Step1: Analyze the condition for constant - speed motion

An object moving at a constant speed has a net force of zero in both the horizontal and vertical directions (Newton's first law: \(F_{net}=ma\), when \(a = 0\), \(F_{net}=0\)).

• Vertical direction: \(F_{norm}=F_{grav}\) (balanced forces in the vertical direction).
• Horizontal direction: If there is a frictional force (\(F_{frict}\)), then \(F_{app}=F_{frict}\) (balanced forces in the horizontal direction).

Step2: Analyze each object

• Object A: Only vertical forces (\(F_{norm}\) and \(F_{grav}\)). No information about horizontal motion. But if we assume no horizontal forces (or no acceleration in the horizontal direction), it can move at a constant speed (e.g., if it was already in motion and there is no un - balanced horizontal force to change its state).
• Object B: \(F_{app}\) is un - balanced in the horizontal direction (\(F_{frict}=0\) in the diagram). So, \(F_{net,x}=F_{app}

eq0\). By Newton's second law \(a=\frac{F_{net}}{m}\), it will have an acceleration in the direction of \(F_{app}\) and not move at a constant speed.

• Object C: In the vertical direction \(F_{norm}=F_{grav}\), and in the horizontal direction \(F_{app}=F_{frict}\). So, \(F_{net,x}=F_{app}-F_{frict}=0\) and \(F_{net,y}=F_{norm}-F_{grav}=0\). The object can move at a constant speed.
• Object D: In the vertical direction \(F_{norm}=F_{grav}\), but \(F_{app}>F_{frict}\). So, \(F_{net,x}=F_{app}-F_{frict}>0\). By Newton's second law \(a=\frac{F_{net}}{m}\), it will have an acceleration in the direction of \(F_{app}\) and not move at a constant speed.
• Object E: \(F_{frict}\) is un - balanced in the horizontal direction (\(F_{app}=0\) in the diagram). So, \(F_{net,x}=F_{frict}

eq0\). By Newton's second law \(a = \frac{F_{net}}{m}\), it will have an acceleration in the direction of \(F_{frict}\) and not move at a constant speed.

Answer:

A. Object A, C. Object C