AP Physics 1- 2.7 Kinetic and Static Friction - Exam Style questions - FRQs- New Syllabus
Kinetic and Static Friction AP Physics 1 FRQ
Unit: 2. Force and Translational Dynamics
Weightage : 10-15%
Question
| Lab Group Number | Coefficient of Kinetic Friction | Coefficient of Static Friction |
|---|---|---|
| \(1\) | \(0.45\) | \(0.54\) |
| \(2\) | \(0.46\) | \(0.52\) |
| \(3\) | \(0.42\) | \(0.56\) |
| \(4\) | \(0.43\) | \(0.55\) |
| \(5\) | \(0.74\) | \(0.23\) |
| \(6\) | \(0.44\) | \(0.54\) |
| Average | \(0.49\) | \(0.49\) |
Most-appropriate topic codes (AP Physics \(1\)):
• Topic \(2.5\) — Newton’s Second Law (Part \( \mathrm{(b)} \))
• Topic \(2.7\) — Kinetic and Static Friction (Part \( \mathrm{(a)} \), Part \( \mathrm{(b)} \), Part \( \mathrm{(c)} \), Part \( \mathrm{(d)} \))
▶️ Answer/Explanation
(a)(i)
A valid setup is an adjustable inclined board with the wood block resting on it. Slowly raise one end of the board until the block just begins to slide.
Measure the angle \(\theta\) that the board makes with the horizontal using a protractor or angle-measuring app. The measured quantity is the critical angle \(\theta\), the angle at which the block is just about to move.
A simple diagram should show the board tilted at angle \(\theta\), the block on the board, and a protractor used to measure \(\theta\).
(a)(ii)
Place the block at rest on the board. Slowly lift one end of the board until the block just begins to slide. Record the angle \(\theta\) at that instant.
To reduce uncertainty, repeat the trial several times and use the average value of \(\theta\). The block can also be placed at different locations on the board to check that the result is not caused by one unusual rough or smooth section of the board.
(b)
At the instant the block is just about to slide, static friction is at its maximum value.
Along the direction parallel to the incline:
\(mg\sin\theta=f_s\)
At the threshold of slipping,
\(f_s=f_{s,\max}=\mu_sN\)
Perpendicular to the incline:
\(N=mg\cos\theta\)
Substitute into the parallel-force equation:
\(mg\sin\theta=\mu_smg\cos\theta\)
Divide both sides by \(mg\cos\theta\):
\(\mu_s=\dfrac{\sin\theta}{\cos\theta}\)
\(\boxed{\mu_s=\tan\theta}\)
(c)
\(\boxed{\text{The static and kinetic coefficients are not equal.}}\)
Group \(5\) is an outlier because its kinetic friction value, \(0.74\), is much larger than the other kinetic friction values, and its static friction value, \(0.23\), is much smaller than the other static friction values.
If group \(5\) is removed, the remaining groups show a consistent pattern: the static friction coefficient is about \(0.52\) to \(0.56\), while the kinetic friction coefficient is about \(0.42\) to \(0.46\). Therefore, the data support the conclusion that the coefficients are different.
(d)
\(\boxed{\text{Remain the same}}\)
The coefficient of static friction is a property of the two surfaces in contact. Since the same wood block bottom is still in contact with the same wood board, the coefficient \(\mu_s\) does not depend on the mass of the block-disk system.
Adding the metal disk increases the normal force and therefore increases the maximum static friction force, since \(f_{s,\max}=\mu_sN\). However, the coefficient \(\mu_s\) itself remains the same.