Question

The box of a well-known breakfast cereal states that one ounce of the cereal contains 113 Calories (1 food Calorie = 4186 J). If 1.79% 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 1.90 m?

Answer 1

Answer:

4456.33N

Explanation:

Let the energy converted by the lifter's body into work done be E.

The work done in lifting the barbell is against gravity and it is given by equation (1);

$work done=mgh..................(1)$

where m is the mass of the barbell, g is acceleration due to gravity and h is the vertical distance (height) through which it is lifted. Hence by the principle of energy conversion as specified by the problem we could write the following equation;

$E=mgh.....................(2)$

Also, it should be recalled that the weight, W of an object is given by the equation below;

$W=mg...............(3)$

Substituting (3) into (2) we obtain the following;

$E=Wh..................(4)$

Given; h = 1.9m

To obtain the energy E converted by the lifter's body in Joules, we use the specifications given in the problem as follows;

Given; 1cal = 4186J

therefore 113cal = (113 x 4186)J = 473018J. This is the total energy contained in one ounce of cereal consumed by the lifter. However as specified by the problem, only 1.79% of this energy was converted by the lifter's body into weight lifting, therefore;

$E=\frac{1.79}{100}*473018J=8467.02J$

Putting this value of E into equation (4), we obtain the following;

$8467.02=W*1.9$

therefore;

$W=\frac{8467.02}{1.9}=4456.33N$

This is the heaviest weight of barbell the lifter could lift with the amount of energy specified.

Answer 2

Answer:

$m=454.73 kg$

Explanation:

To convert the energy of the cereal to know the weight:

$m*g*h=Q'$

$Cal=0.0179*113 Cal=2.0227Cal$

$Q'=2.0227Cal*\frac{4186J}{1Cal}$

$m*g*h=8467.02J$

$m*g=\frac{Q'}{h}=\frac{8467.02J}{1.90m}$

$m*g=4456.33 N$

Supuse the gravity as a g=9.8m/s^2

$m=\frac{4456.33N}{9.8m/s^2}$

$m=454.73 kg$