Question

multiple choice question
which explanation best describes what is occurring in the diagram?
the book accelerates in a random direction because the force exerted by the hand is unbalanced.
the hand exerts a force on the book which is balanced by friction with the table.
the hand exerts a balanced force on the book, causing it to move with constant velocity in the same direction as the force.
the hand exerts an unbalanced force on the book, causing it to accelerate in the same direction as the force.

Explanation:

Step1: Analyze the motion of the book

From the diagram, the velocity \(v\) of the book is increasing over time (\(t = 0s\) to \(t=2.0s\)). According to Newton's second law \(F = ma\) (where \(F\) is the net force, \(m\) is the mass, and \(a\) is the acceleration). When \(a
eq0\), there is a non - zero net force.

Step2: Evaluate each option

• Option 1: The acceleration is in the direction of the force (not random). So, this option is wrong.
• Option 2: If the force exerted by the hand is balanced by friction (\(F = f\)), then \(a = 0\) (from \(F_{net}=F - f=0\)). But the book is accelerating (\(a

eq0\)), so this option is wrong.

• Option 3: If the force is balanced (\(F_{net}=0\)), then \(a = 0\) (constant velocity). But the book is accelerating (\(a

eq0\)), so this option is wrong.

• Option 4: An unbalanced force (\(F_{net}

eq0\)) causes an acceleration (\(a=\frac{F_{net}}{m}\)) in the direction of the net force. This is in line with Newton's second law \(F = ma\).

Answer:

The hand exerts an unbalanced force on the book, causing it to accelerate in the same direction as the force.