Let's analyze the problem and statements one by one.

Given:

• Equation for work: $W = F \cdot d$, where:

  • $W$ is the work in joules (J),
  • $F$ is the force in newtons (N),
  • $d$ is the distance in meters (m).

• Bernie: Pushes with a force of 20 N.

• Hilary: Pushes for a distance of 1.5 m and does 40.5 J of work.

Solve for Hilary's Force:

Using the equation $W = F \cdot d$: $F = \frac{W}{d} = \frac{40.5}{1.5} = 27 \, \text{N}.$ Hilary pushes her box with a force of 27 N.

Evaluate Statements:

1. "An equation to calculate force is $F = \frac{W}{d}$":

   • This is true, as derived directly from $W = F \cdot d$.

2. "Hilary pushes her box with a force of 60.75 N":

   • This is false; Hilary's calculated force is 27 N.

3. "Hilary pushes her box with a greater force than Bernie":

   • True, because Hilary's force (27 N) is greater than Bernie's force (20 N).

Final Answers:

1. True
2. False
3. True

Would you like a detailed explanation of any part?

Related Questions:

1. How is work calculated in physics, and what does it represent?
2. Why is Hilary's force greater even if her distance is less than Bernie's?
3. What are the units of work, force, and distance in the SI system?
4. How does force differ from work conceptually?
5. Can work be done without moving the object? Why or why not?

Tip:

Always ensure all quantities (force, distance, work) are in compatible units before performing calculations.