While rearranging a dorm room, a student does 310 J of work in moving a desk 1.5 m. What was the magnitude of the applied horizontal force?

work = force * distance in direction of force

310 = force * 1.5

force = 310 J/1.5 m = 207 Newtons

207N

To find the magnitude of the applied horizontal force, we need to use the equation for work:

Work (W) = Force (F) × Distance (d) × cos(θ)

Where:
- Work is measured in joules (J)
- Force is the magnitude of the applied force in Newtons (N)
- Distance is the displacement in meters (m)
- θ (theta) is the angle between the force and the displacement (in this case, it's horizontal, so θ is 0 degrees)

In this case, we are given the work (310 J) and the distance (1.5 m). Since the force is in the horizontal direction, the angle θ is 0 degrees. Let's substitute the given values into the equation and solve for the force:

310 J = F × 1.5 m × cos(0°)

cos(0°) is equal to 1, so the equation simplifies to:

310 J = F × 1.5 m

To solve for the force F, divide both sides of the equation by 1.5 m:

F = 310 J / 1.5 m
F = 206.67 N

Therefore, the magnitude of the applied horizontal force is approximately 206.67 Newtons.