Here are the solutions to the problems: 2. A man uses a rope to pull a crate across the floor. The rope forms an angle of 35° to the horizontal. If the man exerts a tensile force of 500 N on the rope, determine the magnitude of the force with which the man: Given: Magnitude of the force, $F = 500$ N Angle to the horizontal, $\theta = 35°$ 2.1 tends to cause the crate to move horizontally. This is the horizontal component of the force. Step 1: Calculate the horizontal component ($F_x$). $$F_x = F \cos \theta$$ $$F_x = 500 \text{ N} \times \cos(35°)$$ $$F_x \approx 500 \text{ N} \times 0.81915$$ $$F_x \approx 409.58 \text{ N}$$ The magnitude of the force that tends to cause the crate to move horizontally is $\boxed{\text{409.58 N}}$. 2.2 tends to cause the crate to lift vertically. This is the vertical component of the force. Step 1: Calculate the vertical component ($F_y$). $$F_y = F \sin \theta$$ $$F_y = 500 \text{ N} \times \sin(35°)$$ $$F_y \approx 500 \text{ N} \times 0.57358$$ $$F_y \approx 286.79 \text{ N}$$ The magnitude of the force that tends to cause the crate to lift vertically is $\boxed{\text{286.79 N}}$.