The human brain consumes about 21.3 W of power under normal conditions. (More power may be required during exams...) How long can a candy bar (299 Calories) power the normally functioning brain? Note: The nutritional Calorie is equivalent to 1000 calories, or 1 kcal, as defined in physics; 1 kcal = 4186 J.

How fast must you lift a 3.60 kg container of milk if the power output of your arm is to be 21.3 W?

i used the eqn P=W/T and i did some unit conversions to get the 299 calories into Joules but the answer is wrong...

A candy bar has 299,000 (gram)-calories or 1.252*10^6 J.

Set 21.3 J/s * T = 1.252*10^6 J
and solve for the time T, in seconds

To determine how long a candy bar can power the brain, we need to convert the energy content of the candy bar into joules.

First, let's convert the calories to joules:
299 Calories * 1000 calories/Calorie * 4186 J/calorie = 1,253,914 J (rounded to the nearest whole number)

Now, we can calculate the time the candy bar can power the brain by dividing the energy in joules by the brain's power consumption:
1,253,914 J / 21.3 W = 58,878 seconds

Therefore, a candy bar can power the normally functioning brain for approximately 58,878 seconds, or around 16.3 hours.

Moving on to the next question about lifting a container of milk:

The power output of your arm is given as 21.3 W, and we need to determine the lifting speed of a 3.60 kg container of milk.

Power is defined as the rate at which work is done, which is equal to the force applied multiplied by the distance traveled per unit of time. In this case, we need to find the lifting speed, which is the distance traveled per unit time.

Using the equation for power, we can rearrange it to solve for distance traveled per unit time:

Power = (Force * Distance) / Time

Rearranging:

Distance/Time = Power / Force

Since the distance traveled per unit time is equivalent to speed, we can say:

Speed = Power / Force

Now we can substitute the given values into the equation:

Speed = 21.3 W / 3.60 kg

Speed = 5.92 m/s

Therefore, to lift a 3.60 kg container of milk using an arm with a power output of 21.3 W, the speed at which you need to lift it is approximately 5.92 m/s.

To answer the first question, we need to convert the energy content of the candy bar from calories to joules. Since 1 nutritional calorie (Cal) is equivalent to 4186 joules (J), we can do the following calculation:

299 Calories * 4186 J/Cal = 1,252,014 J

Now we have the energy content of the candy bar in joules. To find out how long it can power the brain, we need to divide the energy by the power consumed by the brain.

Duration = Energy / Power

Duration = 1,252,014 J / 21.3 W

Calculating this, we get:

Duration ≈ 58,743 seconds

Converting this to minutes:

Duration ≈ 58,743 seconds / 60 seconds/minute

Duration ≈ 979 minutes

Therefore, a candy bar with 299 Calories can power a normally functioning brain for approximately 979 minutes.

Moving on to the second question, to find out how fast you must lift the 3.60 kg container of milk, we need to use the formula:

Power = Force * Velocity

In this case, the power output of your arm is given as 21.3 W. Assuming you are solely lifting the container vertically, the force required will be equal to the weight of the container, given by:

Force = Mass * Gravity

Here, the mass of the container is 3.60 kg, and the acceleration due to gravity is approximately 9.8 m/s².

Substituting these values into the formula, we have:

21.3 W = (3.60 kg * 9.8 m/s²) * Velocity

Simplifying, we get:

21.3 W = 35.28 kg·m²/s³ * Velocity

To solve for the velocity, we divide both sides by 35.28 kg·m²/s³:

Velocity = 21.3 W / 35.28 kg·m²/s³

Calculating this, we find:

Velocity ≈ 0.603 m/s

Therefore, to achieve a power output of 21.3 W when lifting a 3.60 kg container of milk, you need to lift it at a speed of approximately 0.603 m/s.