Work is just force times distance, in this case the force(against gravity) equal to their weight.

Power is work per time: P=W/t

Since the first person climbs the stairs in a shorter period of time, he (or she) uses more power.

Question

asked 2021-03-06

Energy is conventionally measured in Calories as well as in joules.One Calorie in nutrition is 1 kilocalorie, which we define inChapter 11 as 1 kcal = 4,186 J. Metabolizing 1 gram of fat canrelease 9.00 kcal. A student decides to try to lose weight byexercising. She plans to run up and down the stairs in a footballstadium as fast as she can and as many times as necessary. Is thisin itself a practical way to lose weight?

yes

no

To evaluate the program, suppose she runs up a flight of90 steps, each 0.150 m high, in67.0 s. For simplicity, ignore theenergy she uses in coming down (which is small). Assume that atypical efficiency for human muscles is 20.0%. This means that whenyour body converts 100 J from metabolizing fat, 20 J goes intodoing mechanical work (here, climbing stairs). The remainder goesinto internal energy. Assume the student's mass is 57.0 kg.

(a) How many times must she run the flight ofstairs to lose 1 pound of fat?

(b) What is her average power output, in watts and in horsepower,as she is running up the stairs?

W

hp

yes

no

To evaluate the program, suppose she runs up a flight of90 steps, each 0.150 m high, in67.0 s. For simplicity, ignore theenergy she uses in coming down (which is small). Assume that atypical efficiency for human muscles is 20.0%. This means that whenyour body converts 100 J from metabolizing fat, 20 J goes intodoing mechanical work (here, climbing stairs). The remainder goesinto internal energy. Assume the student's mass is 57.0 kg.

(a) How many times must she run the flight ofstairs to lose 1 pound of fat?

(b) What is her average power output, in watts and in horsepower,as she is running up the stairs?

W

hp

asked 2021-02-19

A 10 kg objectexperiences a horizontal force which causes it to accelerate at 5 \(\displaystyle\frac{{m}}{{s}^{{2}}}\), moving it a distance of 20 m, horizontally.How much work is done by the force?

A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?

A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?

A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?

What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?

A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?

A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).

A ball is connected to a rope and swung around in uniform circular motion.The tension in the rope is measured at 10 N and the radius of thecircle is 1 m. How much work is done in one revolution around the circle?

A 10 kg weight issuspended in the air by a strong cable. How much work is done, perunit time, in suspending the weight?

A 5 kg block is moved up a 30 degree incline by a force of 50 N, parallel to the incline. The coefficient of kinetic friction between the block and the incline is .25. How much work is done by the 50 N force in moving the block a distance of 10 meters? What is the total workdone on the block over the same distance?

What is the kinetic energy of a 2 kg ball that travels a distance of 50 metersin 5 seconds?

A ball is thrown vertically with a velocity of 25 m/s. How high does it go? What is its velocity when it reaches a height of 25 m?

A ball with enough speed can complete a vertical loop. With what speed must the ballenter the loop to complete a 2 m loop? (Keep in mind that the velocity of the ball is not constant throughout the loop).

asked 2021-03-16

One heater uses 340 W of power when connected by itself to abattery. Another heater uses 247 W ofpower when connected by itself to the same battery. How much totalpower do the heaters use when they are both connected in seriesacross the battery?

asked 2021-06-03

In government data, a household consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States. \(\text{Number of people}\ \begin{array}{|l|c|c|c|c|c|c|c|} \hline & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{array}{l} \text { Household } \\ \text { probability } \end{array} & 0.25 & 0.32 & 0.17 & 0.15 & 0.07 & 0.03 & 0.01 \\ \hline \begin{array}{l} \text { Family } \\ \text { probability } \end{array} & 0 & 0.42 & 0.23 & 0.21 & 0.09 & 0.03 & 0.02 \\ \hline \end{array}\)

Let \(H =\) the number of people in a randomly selected U.S. household and \(F =\) the number of people in a randomly chosen U.S. family. Find the expected value of each random variable. Explain why this difference makes sense.