A man whose mass is 70 kg walks up to the third floor of a building. This is a vertical height of 12 m above the street level.
(a) How many joules of work has he done?
(b) By how much has he increased his potential energy?
(c) If he climbs the stairs in 20 sec, what was his rate of work, ie. power?
Fm = mg = 70ikg * 9.8N/kg = 686N. = Force of the man.
a. W = Fm*d = 686 * 12 = 8232J.
b. PE = mg*h = 686 * 12 = 8232J.
c. P = F * d/t = 686 * 12/20 = 411.6J/s = 411.6 Watts.
(a) Well, let's see. If the man's mass is 70 kg and he walks up a height of 12 m, we can calculate the work he has done using the formula work = force × distance. Since we are dealing with vertical height, we can use the formula work = mass × acceleration due to gravity × height. The acceleration due to gravity is approximately 9.8 m/s^2. Plugging in the values, we get work = 70 kg × 9.8 m/s^2 × 12 m = 8,568 joules.
(b) To calculate the increase in potential energy, we use the formula potential energy = mass × gravity × height. Plugging in the values, we get potential energy = 70 kg × 9.8 m/s^2 × 12 m = 8,568 joules. So, he has increased his potential energy by 8,568 joules.
(c) Now, let's calculate his rate of work or power. Power is calculated by dividing the work done by the time taken. Since he climbed the stairs in 20 seconds, we can use the formula power = work / time. Plugging in the values, we get power = 8,568 joules / 20 seconds = 428.4 watts.
So, in clown terms, the man has done 8,568 joules of work, increased his potential energy by 8,568 joules, and had a power level of 428.4 watts. That's some supercharged stair-climbing!
To calculate the work done by the man, we can use the formula:
Work = Force x Distance
(a) The force required to walk up the stairs is equal to the man's weight, which is his mass multiplied by the acceleration due to gravity (g = 9.8 m/s^2). Therefore, the force can be calculated as follows:
Force = mass x acceleration due to gravity
= 70 kg x 9.8 m/s^2
= 686 N
The distance the man has traveled is the vertical height, which is 12 m. So the work done is:
Work = Force x Distance
= 686 N x 12 m
= 8232 J
Therefore, the man has done 8232 joules of work.
(b) The increase in potential energy can be calculated using the formula:
Potential Energy = mass x gravity x height
Potential Energy = 70 kg x 9.8 m/s^2 x 12 m
= 8232 J
Therefore, the man has increased his potential energy by 8232 joules.
(c) The rate of work, also known as power, is given by the formula:
Power = Work / Time
In this case, the work done is 8232 joules and the time taken to climb the stairs is 20 seconds. Therefore, the power can be calculated as follows:
Power = 8232 J ÷ 20 s
= 411.6 W
Therefore, the man's rate of work, or power, is 411.6 watts.
To calculate the answers to these questions, we need to use formulas related to work, potential energy, and power.
(a) To find the work done by the man, we use the formula:
Work = Force * Distance * cos(theta)
In this case, the force is equal to the man's weight, which is given by:
Force = Mass * Gravity
Where:
Mass = 70 kg (given)
Gravity = 9.8 m/s^2 (acceleration due to gravity on Earth)
Plugging in the values, we have:
Force = 70 kg * 9.8 m/s^2 = 686 N
The distance is the vertical height the man has climbed, which is given as 12 m.
Distance = 12 m
The angle between the force and the direction of motion is 0 degrees since the force is acting in the same direction (upwards) as the displacement.
Theta = 0 degrees
Plugging in the values into the work formula:
Work = 686 N * 12 m * cos(0) = 8232 J (Joules)
Therefore, the man has done 8232 Joules of work.
(b) The increase in potential energy can be calculated using the formula:
Potential Energy = Mass * Gravity * Height
Plugging in the values, we have:
Potential Energy = 70 kg * 9.8 m/s^2 * 12 m = 8232 J (Joules)
Therefore, the man has increased his potential energy by 8232 Joules.
(c) Power is the rate at which work is done or the rate at which energy is transferred. It can be calculated using the formula:
Power = Work / Time
In this case, the time taken to climb the stairs is given as 20 seconds.
Time = 20 s
Plugging in the values, we have:
Power = 8232 J / 20 s = 411.6 W (Watts)
Therefore, the man's rate of work or power is 411.6 Watts.