* Rolling is a combination of linear and circular motion. In order to study rolling motion, we perform the following experiment. We mark three points A. B, and C on a bicycle wheel and observe how these points move while the bicycle is pushed forward 2 cm, a distance much smaller than the radius of the wheel. Figure P5.11 shows a long-exposure photo of the experiment. The camera (i.e., the observer) is standing still on the ground. A is the point where the wheel is initially touching the ground. B is the point at the wheel’s axis, and C is the point on the top of the wheel, directly above point A (a) Determine the displacements of points A. B. and C as observed by the stationary observer. (Hint: Use similar tangles.) (b) Using your answers from part (a), determine the speed of the points A, B, and C with respect to the ground for the bicycle that is moving at constant speed v How would the answers to part (b) change if the observer were moving in the same direction as the bicycle but (c) with the same speed as the bicycle or (d) twice as fast as the bicycle?
* Rolling is a combination of linear and circular motion. In order to study rolling motion, we perform the following experiment. We mark three points A. B, and C on a bicycle wheel and observe how these points move while the bicycle is pushed forward 2 cm, a distance much smaller than the radius of the wheel. Figure P5.11 shows a long-exposure photo of the experiment. The camera (i.e., the observer) is standing still on the ground. A is the point where the wheel is initially touching the ground. B is the point at the wheel’s axis, and C is the point on the top of the wheel, directly above point A (a) Determine the displacements of points A. B. and C as observed by the stationary observer. (Hint: Use similar tangles.) (b) Using your answers from part (a), determine the speed of the points A, B, and C with respect to the ground for the bicycle that is moving at constant speed v How would the answers to part (b) change if the observer were moving in the same direction as the bicycle but (c) with the same speed as the bicycle or (d) twice as fast as the bicycle?
* Rolling is a combination of linear and circular motion. In order to study rolling motion, we perform the following experiment. We mark three points A. B, and C on a bicycle wheel and observe how these points move while the bicycle is pushed forward 2 cm, a distance much smaller than the radius of the wheel. Figure P5.11 shows a long-exposure photo of the experiment. The camera (i.e., the observer) is standing still on the ground. A is the point where the wheel is initially touching the ground. B is the point at the wheel’s axis, and C is the point on the top of the wheel, directly above point A (a) Determine the displacements of points A. B. and C as observed by the stationary observer. (Hint: Use similar tangles.) (b) Using your answers from part (a), determine the speed of the points A, B, and C with respect to the ground for the bicycle that is moving at constant speed v How would the answers to part (b) change if the observer were moving in the same direction as the bicycle but (c) with the same speed as the bicycle or (d) twice as fast as the bicycle?
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…
Two complex values are z1=8 + 8i, z2=15 + 7 i. z1∗ and z2∗ are the complex conjugate values.
Any complex value can be expessed in the form of a+bi=reiθ. Find r and θ for (z1-z∗2)/z1+z2∗. Find r and θ for (z1−z2∗)z1z2∗ Please show all steps
Chapter 5 Solutions
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