Calculations: (On a separate piece of paper) 1) Calculate the weight (force of gravity) of the student, using F_(g)=ma_(g) 2) Calculate the power of the student, P=W/Delta t for walking the stairs. 3) Calculate the equivalent horsepower of the student (hp). Note: 1hp=745.7W Questions: 1) Would the amount of work walking and running up the stairs be the same? Why? 2) Which would require more power, walking or running up the stairs?Why? 3) How many 60 W CFL lightbulbs could you power, assuming 100% efficiency? 4) In what sports must a person be able to generate a lot of force? Do much work? Develop great power? Name a clear, and different sport for each. (Hint: think of the relevant equations) 5) An average person needs about 2000 food Calories every 24 hours to survive. Calculate their average Power developed over 24 h (Note: 1foodCalorie=4.18kJ ). Remember that W=Delta E, work and energy are equivalent. 6) Using your power,calculate how many minutes you would have to walk stairs in order to "burn off" the energy in a Mars chocolate bar. A Mars bar contains about 190 Calories. (Note 1food Calorie=4.18kJ ). Remember that W=Delta E and assume all the energy is converted into mechanical energy. 7) If you could sell the energy you expended over 1.0 hour of walking stairs to your local Electric Company (assume 100% efficiency), how much money could you make?The price of electricity is 83 cents per 3.6 MJ.

To solve these problems, we need to go through each calculation step by step. Let's start with the calculations:<br /><br />### Calculations<br /><br />1) **Calculate the weight (force of gravity) of the student:**<br /><br /> The formula for the force of gravity is:<br /> \[<br /> F_g = m \cdot a_g<br /> \]<br /> where \( m \) is the mass of the student and \( a_g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).<br /><br /> You need to know the mass of the student to calculate this. For example, if the student's mass is 70 kg:<br /> \[<br /> F_g = 70 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 686.7 \, \text{N}<br /> \]<br /><br />2) **Calculate the power of the student for walking the stairs:**<br /><br /> Power is calculated using:<br /> \[<br /> P = \frac{W}{\Delta t}<br /> \]<br /> where \( W \) is the work done and \( \Delta t \) is the time taken.<br /><br /> Work done \( W \) can be calculated as:<br /> \[<br /> W = F_g \cdot h<br /> \]<br /> where \( h \) is the height of the stairs.<br /><br /> If the height of the stairs is, say, 5 meters, and it takes 10 seconds to walk up:<br /> \[<br /> W = 686.7 \, \text{N} \times 5 \, \text{m} = 3433.5 \, \text{J}<br /> \]<br /> \[<br /> P = \frac{3433.5 \, \text{J}}{10 \, \text{s}} = 343.35 \, \text{W}<br /> \]<br /><br />3) **Calculate the equivalent horsepower of the student:**<br /><br /> Convert watts to horsepower:<br /> \[<br /> hp = \frac{P}{745.7}<br /> \]<br /> \[<br /> hp = \frac{343.35}{745.7} \approx 0.46 \, \text{hp}<br /> \]<br /><br />### Questions<br /><br />1) **Would the amount of work walking and running up the stairs be the same? Why?**<br /><br /> Yes, the amount of work would be the same because work depends on the force applied and the distance moved in the direction of the force. Since both walking and running involve moving the same mass over the same height, the work done is the same.<br /><br />2) **Which would require more power, walking or running up the stairs? Why?**<br /><br /> Running would require more power because power is the rate at which work is done. Since running takes less time than walking to cover the same distance, the power output is higher when running.<br /><br />3) **How many 60 W CFL lightbulbs could you power, assuming 100% efficiency?**<br /><br /> Using the power calculated earlier (343.35 W):<br /> \[<br /> \text{Number of bulbs} = \frac{343.35 \, \text{W}}{60 \, \text{W/bulb}} \approx 5.72<br /> \]<br /> So, you could power approximately 5 lightbulbs continuously.<br /><br />4) **In what sports must a person be able to generate a lot of force, do much work, develop great power?**<br /><br /> - Generate a lot of force: Weightlifting (requires high force to lift heavy weights).<br /> - Do much work: Cycling (sustained effort over long distances).<br /> - Develop great power: Sprinting (requires high power output over short durations).<br /><br />5) **Calculate average power developed over 24 hours:**<br /><br /> An average person needs about 2000 food Calories per day.<br /> \[<br /> 2000 \, \text{Cal} \times 4.18 \, \text{kJ/Cal} = 8360 \, \text{kJ}<br /> \]<br /> Convert to joules:<br /> \[<br /> 8360 \, \text{kJ} = 8,360,000 \, \text{J}<br /> \]<br /> Average power:<br /> \[<br /> P = \frac{8,360,000 \, \text{J}}{24 \times 3600 \, \text{s}} \approx 96.76 \, \text{W}<br /> \]<br /><br />6) **Calculate how many minutes to burn off a Mars bar:**<br /><br /> A Mars bar contains 190 Calories.<br /> \[<br /> 190 \, \text{Cal} \times 4.18 \, \text{kJ/Cal} = 794.2 \, \text{kJ} = 794,200 \, \text{J}<br /> \]<br /> Using the power from walking stairs (343.35 W):<br /> \[<br /> \text{Time} = \frac{794,200 \, \text{J}}{343.35 \, \text{W}} \approx 2313.6 \, \text{s}<br /> \]<br /> Convert to minutes:<br /> \[<br /> \frac{2313.6 \, \text{s}}{60} \approx 38.56 \, \text{minutes}<br /> \]<br /><br />7) **Calculate money made from selling energy:**<br /><br /> Energy expended in 1 hour:<br /> \[<br /> E = 343.35 \, \text{W} \times 3600 \, \text{s} = 1,236,060 \, \text{J} = 1.23606 \, \text{MJ}<br /> \]<br /> Price of electricity is 83 cents per 3.6 MJ:<br /> \[<br /> \text{Money earned} = \frac{1.23606 \, \text{MJ}}{3.6 \, \text{MJ}} \times 0.83 \approx 0.285 \, \text{cents}<br /> \]<br /><br />These calculations provide a comprehensive understanding of the physics involved in the scenario described.