A Golfer Estimates That His Golf Ball Is 250 Yards To The Ho

A Golfer Estimates That His Golfball Is 250 Yards To The Hole At Th

A golfer estimates that his golfball is 250 yards to the hole. At the hole, another golfer has dropped a water bottle that is reflecting light back to the golfer and his ball. What is the approximate time difference based on golfers distance to the hole/water bottle? A CdS photocell has a resistance versus light intensity as shown in the following graph. The cell has a time constant of 25 ms. At t=0, the cell is exposed to a sudden change of light intensity from 20 W/m² to 80 W/m². What is the sensor resistance after 20 ms? A force of 120 pounds-force is used to open a valve. What is the area of the diaphragm if a control gauge of 90 kPa (~13 psi) must provide this force? A processing plant is being proposed that will need to use the city’s water system to be successful. The plant will need a minimum of 2500 gallons of water per minute (gpm) for its operation. The city’s current water supply pipe to the proposed plant is 12 inches in diameter with a water velocity of 1.5 m/s. Will the city’s current water supply meet the plant’s needs or will it need to be upgraded? Show calculations to verify your answer. From the figure below, construct the truth table for the logic diagram. What function does this represent? PLEASE SEE ATTACHMENT

Paper For Above instruction

The scenario presented involves multiple engineering and physics problems encompassing concepts such as light reflection and time delay estimation, photoelectric sensor response, mechanical force calculations, fluid flow analysis, and digital logic design. This paper aims to explore each problem step-by-step, providing detailed calculations, principles, and reasoning to address the questions posed effectively.

Estimating Time Difference via Light Reflection

The first problem involves a golfer estimating the time delay based on the reflection of light from a water bottle back to him and his ball. Light travels approximately 3 x 10^8 meters per second in vacuum. In air, the speed of light is very close to this value, so for practical purposes, we consider the speed of light c = 3 x 10^8 m/s.

The golfer estimates the distance to the hole as 250 yards, which converts to meters (1 yard ≈ 0.9144 meters). Therefore:

  • Distance to hole, d = 250 yards × 0.9144 ≈ 228.6 meters.

The water bottle reflection adds an extra distance the light must travel: from the golfer to the bottle and back. Assuming the bottle is approximately located at the same distance as the hole, the total additional delay is negligible over such a large distance but can be approximated by:

Time delay, Δt = 2 × d / c ≈ 2 × 228.6 / (3 × 10^8) ≈ 1.524 × 10^{-6} seconds, or approximately 1.5 microseconds. Therefore, the approximate time difference the golfer could detect based on light reflection is on the order of a few microseconds, which is not perceptible without precise equipment.

Resistance Change in CdS Photocell

The CdS (Cadmium Sulfide) photocell exhibits a resistance response to light intensity changes. Given a time constant τ = 25 ms, and an initial change in light intensity from 20 W/m² to 80 W/m² at t=0, we want to determine the resistance after 20 ms.

The resistance change follows an exponential response characterized by:

R(t) = R_final + [R_initial - R_final] × e^{-t/τ}

Assuming the resistance decreases as light intensity increases (common for CdS cells), and that at the initial intensity (20 W/m²), resistance is R_initial, and at high intensity (80 W/m²), resistance R_final, the exact resistance values depend on the resistance versus light intensity graph (not provided explicitly here). However, for the purpose of calculation, if R_initial corresponds to the resistance at 20 W/m² and R_final at 80 W/m², then at t = 20 ms:

t = 20 ms = 0.02 s, thus

R(0.02) = R_final + [R_initial - R_final] × e^{-0.02/0.025} ≈ R_final + [R_initial - R_final] × e^{-0.8}

Since e^{-0.8} ≈ 0.449, the resistance after 20 ms is roughly 45% of the difference between initial and final resistance from the resistance at the higher flux state.

Without exact resistance values from the graph, precise numerical results cannot be given here, but this method shows the exponential response characteristic of the photocell.

Mechanical Force and Diaphragm Area Calculation

When a force of 120 pounds-force (lbf) is used to open a valve, and a control gauge reads 90 kPa (~13 psi), we can determine the area of the diaphragm responsible for exerting this force.

The relation is:

Force (F) = Pressure (P) × Area (A)

Expressing all units in consistent SI units:

  • 1 psi ≈ 6.895 kPa, so 13 psi ≈ 13 × 6.895 ≈ 89.635 kPa, close to 90 kPa as given.
  • Force in newtons: 120 lbf = 120 × 4.44822 ≈ 533.79 N.

Rearranging for area:

A = F / P = 533.79 N / (90,000 Pa) ≈ 0.00593 m² or 59.3 cm².

Thus, the diaphragm must have an area of approximately 59.3 square centimeters to produce the required force at the specified pressure.

Water Supply Analysis for Proposed Plant

The plant requires a minimum of 2500 gallons per minute (gpm). The city’s current water pipe has a diameter of 12 inches, and the water velocity is 1.5 m/s. To verify if the current system can supply enough water, calculate the flow capacity of the existing pipe:

The cross-sectional area, A, of the pipe is:

  • Diameter, D = 12 inches = 0.3048 meters.
  • Area, A = π × (D/2)^2 ≈ 3.1416 × (0.1524)^2 ≈ 0.073 m².

Flow rate, Q, is then:

Q = A × v = 0.073 m² × 1.5 m/s ≈ 0.1095 m³/s.

Convert to gpm (1 m³/s ≈ 15,850.3 gpm):

Q ≈ 0.1095 × 15,850.3 ≈ 1,736 gpm.

Since 1,736 gpm

Logic Diagram and Function Identification

Without the specific figure, constructing an exact truth table is not feasible. However, typical logic functions include AND, OR, NAND, NOR, XOR, and XNOR. Based on common logic diagram analysis, the truth table construction involves listing all possible input combinations (0 or 1) and deriving the output according to the logic gates. Once the truth table is complete, the function can be identified by analyzing the output pattern, which might correspond to standard logical operations like conjunction, disjunction, negation, or formed combinations.

Conclusion

The set of problems presented demonstrates key principles across optics, electronics, mechanics, fluid dynamics, and digital logic. Precise calculation and reasoning are essential in engineering applications to make informed decisions, whether estimating time delays due to light speed, calculating sensor responses, designing mechanical components, assessing infrastructure capacity, or decoding logical functions. Each problem emphasizes the interconnectedness of physical principles and the importance of accurate quantitative analysis in engineering practice.

References

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  • Giacomoni, P., & Metaxas, D. (2013). Digital Logic Design. Springer.
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  • Adams, R. (2015). Sensor Technologies and Applications. CRC Press.
  • Stallings, W. (2018). Computer Organization and Architecture. Prentice Hall.

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