The box of a well-known breakfast cereal states that one ounce of the cereal contains 129 Calories (1 food Calorie = 4186 J). If 2.55% of this energy could be converted by a weight lifter's body into work done in lifting a barbell, what is the weight of the heaviest barbell that could be lifted a distance of 1.91 m?
129 Cal * 4186 J/Cal = 536,124 Joules
.0255 * 536,124 = 13,671 Joules
m g h = m g (1.91) = 13,671
so
m g = 7158 Newtons weight
and
m = 730 Kilograms of mass
around 1600 pounds
Well, I'm no weight lifter, but I can give you a humorous answer! Just remember, I'm not a mathematician either!
If 2.55% of the cereal's energy can be converted into work by a weight lifter, then we can calculate the work done by the lifter using the formula:
Work = Energy x Efficiency
The energy in this case would be 129 Calories or 129 x 4186 J. And the efficiency is 2.55% or 0.0255. So, to find the work done, we multiply the energy by the efficiency.
Now, since work is equal to the force exerted by the lifter multiplied by the distance, we can set up the equation:
Work = Force x Distance
And we need to solve for the force or in this case, the weight of the barbell. We know the distance is 1.91 m, so let's plug in the values and solve for the weight of the barbell.
(129 x 4186 J) x 0.0255 = Weight x 1.91 m
Now, if you simplify and do the math, you'll find the weight of the heaviest barbell that could be lifted a distance of 1.91 m. And I'll be here, juggling jokes while you calculate!
To find the weight of the heaviest barbell that could be lifted a distance of 1.91 m, we need to calculate the energy required to lift the barbell.
Step 1: Convert the Calorie to Joules.
1 food Calorie = 4186 J
129 Calories = 129 * 4186 J
Step 2: Calculate the energy converted by the body.
2.55% of 129 * 4186 J = 0.0255 * (129 * 4186 J)
Step 3: Calculate the work done.
Work (W) = Force (F) * Distance (d)
Since work is the product of force and distance, and weight (W) = mass (m) * gravity (g), we can rewrite the formula as:
W = m * g * d
Step 4: Solve for the weight (m).
W = m * g * d
0.0255 * (129 * 4186 J) = m * 9.81 m/s² * 1.91 m
Step 5: Calculate the weight (m).
m = (0.0255 * (129 * 4186 J)) / (9.81 m/s² * 1.91 m)
Now, let's calculate it:
m = (0.0255 * (129 * 4186)) / (9.81 * 1.91)
Using a calculator, the weight of the heaviest barbell that could be lifted a distance of 1.91 m is approximately 218.22 kg.
To calculate the weight of the heaviest barbell that can be lifted, we'll need to use the following steps:
Step 1: Calculate the energy content of one ounce of the breakfast cereal in joules.
Given that 1 food Calorie (C) is equal to 4186 joules (J), and each ounce of the cereal contains 129 Calories, we can calculate the energy content of one ounce of the cereal as follows:
Energy_content = 129 C * 4186 J/C
Step 2: Determine the amount of energy that can be converted into work.
The problem states that only 2.55% of the energy can be converted by the lifter's body into work. Therefore, we need to calculate the energy available for work:
Energy_available = 0.0255 * Energy_content
Step 3: Calculate the work done in lifting the barbell.
The work done in lifting the barbell can be calculated using the formula:
Work = Force * Distance
Since work is equal to the energy available, and distance is given as 1.91 m, we can rearrange the formula to solve for the force:
Force = Work / Distance
Force = Energy_available / Distance
Step 4: Convert the force into weight.
Since weight is the force acting on an object, we divide the force by the acceleration due to gravity (9.8 m/s^2) to get the weight:
Weight = Force / 9.8 m/s^2
Substituting the values we have:
Weight = (Energy_available / Distance) / 9.8 m/s^2
Now, we can calculate the weight of the heaviest barbell that can be lifted using the given information.