Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, θ C , called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to μ s n for angles less than θ C ? Explain. What can you definitely say about the magnitude of the friction force for any angle θ ≤ θ c ? (c) Show that the coefficient of static friction is given by μ s = tan θ c . (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value θ c ’ ≤ θ c such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction? Figure P4.82
Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, θ C , called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to μ s n for angles less than θ C ? Explain. What can you definitely say about the magnitude of the friction force for any angle θ ≤ θ c ? (c) Show that the coefficient of static friction is given by μ s = tan θ c . (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value θ c ’ ≤ θ c such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction? Figure P4.82
Solution Summary: The author explains how the friction force, normal force and weight are the forces acting on the coin.
Measuring coefficients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.82. The angle of the incline, θC, called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to μsn for angles less than θC? Explain. What can you definitely say about the magnitude of the friction force for any angle θ ≤ θc? (c) Show that the coefficient of static friction is given by μs = tan θc. (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value θc’ ≤ θc such that the coin moves down the incline with constant speed. How does observation enable you to obtain the coefficient of kinetic friction?
Figure P4.82
Definition Definition Force that opposes motion when the surface of one item rubs against the surface of another. The unit of force of friction is same as the unit of force.
How can you tell which vowel is being produced here ( “ee,” “ah,” or “oo”)? Also, how would you be able to tell for the other vowels?
You want to fabricate a soft microfluidic chip like the one below. How would you go about
fabricating this chip knowing that you are targeting a channel with a square cross-sectional
profile of 200 μm by 200 μm. What materials and steps would you use and why? Disregard the
process to form the inlet and outlet.
Square Cross Section
1. What are the key steps involved in the fabrication of a semiconductor device.
2. You are hired by a chip manufacturing company, and you are asked to prepare a silicon wafer
with the pattern below. Describe the process you would use.
High Aspect
Ratio
Trenches
Undoped Si Wafer
P-doped Si
3. You would like to deposit material within a high aspect ratio trench. What approach would you
use and why?
4. A person is setting up a small clean room space to carry out an outreach activity to educate high
school students about patterning using photolithography. They obtained a positive photoresist, a
used spin coater, a high energy light lamp for exposure and ordered a plastic transparency mask
with a pattern on it to reduce cost. Upon trying this set up multiple times they find that the full
resist gets developed, and they are unable to transfer the pattern onto the resist. Help them
troubleshoot and find out why pattern of transfer has not been successful.
5. You are given a composite…
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.