Answer :

Sure! Let's solve the problem step-by-step.

James is doing work to move a bag of gravel. The work done is related to the force applied and the distance the object is moved.

Here's how you can find the distance:

1. Understand the formula for work:

Work (W) is calculated using the formula:
[tex]\[
W = F \times d
\][/tex]
where:
- [tex]\( W \)[/tex] is the work done, in joules (J),
- [tex]\( F \)[/tex] is the force applied, in newtons (N),
- [tex]\( d \)[/tex] is the distance, in meters (m).

2. Relate force to mass and gravity:

The force (F) needed to move an object is calculated using the equation:
[tex]\[
F = m \times g
\][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object, in kilograms (kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity, approximately [tex]\( 9.8 \, \text{m/s}^2 \)[/tex].

3. Substitute force in the work formula:

Since force is mass times gravity, the work formula can be rewritten as:
[tex]\[
W = m \times g \times d
\][/tex]
Now we know:
- [tex]\( W = 67 \, \text{Joules} \)[/tex],
- [tex]\( m = 108 \, \text{kg} \)[/tex],
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex].

4. Solve for distance (d):

Rearrange the equation to solve for distance (d):
[tex]\[
d = \frac{W}{m \times g}
\][/tex]

5. Calculate the distance:

Substitute the known values into the equation:
[tex]\[
d = \frac{67}{108 \times 9.8}
\][/tex]

6. Get the result:

By calculating the above expression, you find that the distance James moves the bag is approximately [tex]\( 0.0633 \)[/tex] meters.

So, James moves the bag of gravel about 0.0633 meters.

Other Questions