Question

Two students push a heavy crate across the floor. John pushes with a force of 185 N due east and Joan pushes with a force of 165 N at 30∘north of east. What is the resultant horizontal force on the crate?

Answer 1

To find the resultant horizontal force on the crate, calculate Joan's horizontal force component and add it to John's eastward force. The vertical component is irrelevant for horizontal force calculation.

Step-by-step explanation:

To determine the resultant horizontal force on the crate, we must add the forces vectorially. John's force is strictly horizontal, pointing due east, with a magnitude of 185 N. Joan's force must be broken down into horizontal and vertical components. Since Joan's force is at a 30° angle north of east, the horizontal component (FJoan,x) can be found using cosine:

FJoan,x = 165 N × cos(30°)

The vertical component is not needed for the horizontal resultant force. Once we calculate FJoan,x, we sum it with John's force:

Fresultant,x = 185 N + FJoan,x

Performing the calculations will yield the total horizontal force on the crate.

Answer 2

327.894 N

Step-by-step explanation:

We have given two forces Jhon pushes with a force of 185 N in east direction and Joan pushes with a force of 165 N at 30° north of east which is clearly shown in figure

We fave to find the total horizontal force

So total horizontal force will be
`F_X=185+165cos30^(\circ)` =327.894 N ( total horizontal force will be sum of force in the east direction and horizontal component of the force in north- east direction)