Here is the solution to the problem: 7.5 What is the magnitude and direction of the horizontal force that counters the movement of the roller (i.e. the frictional force between the roller and the lawn)? Given: The roller is pushed at a constant speed. This means the net force acting on the roller is zero, according to Newton's First Law. Step 1: Identify the horizontal forces. The horizontal forces are the horizontal component of the applied force ($F_x$) and the frictional force ($F_f$). From part 7.1, the horizontal component of the applied force is $F_x = 200$ N. This force acts in the direction of motion (forward). Step 2: Apply the condition for constant speed. Since the roller is moving at a constant speed, the net horizontal force is zero. This means the forward force must be balanced by the backward force. $$F_x - F_f = 0$$ $$F_f = F_x$$ $$F_f = 200 \text{ N}$$ Step 3: Determine the direction of the frictional force. Frictional force always opposes the direction of motion. Since the roller is moving forward, the frictional force acts backward. The magnitude of the frictional force is $\boxed{\text{200 N}}$ and its direction is $\boxed{\text{opposite to the direction of motion (backward)}}$. That's 2 down. 3 left today — send the next one.