A man pushes with a force of 310 N on a box at an angle of 55 degrees to the floor. How much of the force is directed into the floor, making his job more difficult?

178 N(my choice)
254 N
300 N
150 N

B. 254 N

To determine how much of the force is directed into the floor, we can use trigonometry.

Step 1: Identify the given information:
- The force applied by the man: 310 N
- The angle of the force with the floor: 55 degrees

Step 2: Use trigonometry to find the component of the force directed into the floor:
The force directed into the floor can be found using the formula:
Force into the floor = Force * cosine(angle)

Force into the floor = 310 N * cosine(55 degrees)

Step 3: Use a calculator to find the cosine of the given angle:
cosine(55 degrees) ≈ 0.573576436

Step 4: Substitute the value into the formula:
Force into the floor = 310 N * 0.573576436

Step 5: Calculate the force into the floor:
Force into the floor ≈ 177.8385 N

Therefore, approximately 178 N of the force is directed into the floor, making the man's job more difficult.

To determine how much of the force is directed into the floor, we need to find the component of the force in the direction perpendicular to the floor. This can be calculated using trigonometry.

The force that the man applies can be broken down into two components: one that acts parallel to the floor and one that acts perpendicular to the floor.

The component of the force that acts perpendicular to the floor can be found using the formula:
F_perpendicular = F * sin(theta)

Where:
F_perpendicular is the component of the force perpendicular to the floor
F is the magnitude of the force (310 N in this case)
Theta is the angle between the force and the floor (55 degrees in this case)

Substituting the values into the formula, we get:
F_perpendicular = 310 N * sin(55 degrees) ≈ 251.19 N

Therefore, approximately 251.19 N of the force is directed into the floor, making the man's job more difficult.

So, the correct answer is 251 N, not one of the options provided.

F = 310 * sin55.