What is the total work done on the crate?

Steps to Solve

1. Calculate the Normal Force

Since the crate is on a level surface, the normal force ($F_N$) is equal to the weight of the crate. The weight can be calculated using the formula:

$$ F_N = m \cdot g $$

where:

• $m = 28.9 , \text{kg}$ (mass of the crate)
• $g = 9.81 , \text{m/s}^2$ (acceleration due to gravity)

2. Determine the Force of Friction

Now, we can find the force of friction ($F_f$) using the equation:

$$ F_f = \mu_k \cdot F_N $$

where:

• $\mu_k = 0.26$ (coefficient of kinetic friction)

3. Plug in the Normal Force

First, calculate the normal force:

$$ F_N = 28.9 \cdot 9.81 $$

Then, substitute into the friction formula:

$$ F_f = 0.26 \cdot F_N $$

4. Calculate the Work Done Against Friction

Work done ($W$) against friction can be computed using the formula:

$$ W = F_f \cdot d $$

where:

• $d = 4.85 , \text{m}$ (distance the crate is pushed)

5. Combine the Formulas to Find Work Done

From steps 2 & 4, the total work done can be expressed as:

$$ W = 0.26 \cdot (m \cdot g) \cdot d $$

6. Final Calculation

Now substitute the values into the final equation:

$$ W = 0.26 \cdot (28.9 \cdot 9.81) \cdot 4.85 $$