Question

during a workout, a person repeatedly lifts a 12 - lb barbell through a distance of 1.3 ft. how manyreps of this lift are required to burn off 150 calories (c)?

a. 6.6×10^4
b. 3.0×10^4
c. 4.2×10^2
d. 8.1×10^3
e. 1.1×10^6

Explanation:

Step1: Calculate work done per rep

Work done in lifting an object is given by $W = Fd$, where $F$ is the force and $d$ is the distance. The force here is equal to the weight of the barbell. Given weight $F= 12\ lb$ and distance $d = 1.3\ ft$, so work done per rep $W_{rep}=12\times1.3=15.6\ ft - lb$.

Step2: Convert calories to ft - lb

We know that $1\ Calorie= 2646\ ft - lb$. So, $150\ Calories$ is equal to $150\times2646 = 396900\ ft - lb$.

Step3: Calculate number of reps

Let the number of reps be $n$. Then $n=\frac{\text{Total work}}{\text{Work per rep}}$. So $n=\frac{396900}{15.6}\approx 25442.31$. In scientific - notation, $n\approx 2.544231\times 10^{4}$. But there is an error above, we should use the conversion factor $1\ Cal = 4.184\ J$ and $1\ J= 0.737562\ ft - lb$.
First, convert $150\ Cal$ to joules: $150\ Cal\times4.184\ J/Cal = 627.6\ J$.
Then convert joules to ft - lb: $627.6\ J\times0.737562\ ft - lb/J\approx 463.3\ ft - lb$.
Work per rep $W = 12\times1.3=15.6\ ft - lb$.
Number of reps $n=\frac{463.3}{15.6}\approx 29.7$.
Let's do it in a more standard way.
We know that $1\ Cal=4184\ J$ and $1\ J = 0.737562\ ft - lb$.
$150\ Calories=150\times4184\ J = 627600\ J$.
$627600\ J\times0.737562\ ft - lb/J\approx 463300\ ft - lb$.
Work per rep $W = 12\times1.3 = 15.6\ ft - lb$.
Number of reps $n=\frac{463300}{15.6}\approx 29700\approx 3.0\times 10^{4}$.

Answer:

b. $3.0\times 10^{4}$