From our experiences riding on a bicycle we know that when it is on a slope there is a force that pulls it downhill. To hold the bicycle in place or maintain constant speed we have to provide a balancing force. The size of the unbalanced force (and how hard we have to pull to balance it) depends on the steepness of the hill.
There are several ways to characterize the steepness of an incline. We could measure the angle with respect to a horizontal surface. We could determine the slope, which is the ratio of the increase in height to the amount of horizontal progress (slope = H/L in the diagram). Instead, in this activity we used a different measure: the ratio of the increase in height to the distance traveled along the incline (steepness = H/D). Not only is it easier to measure than the angle, but the force that we measure is exactly proportional to it.
When we attach a scale to the cart on the incline it measures how large a force is needed to hold the cart at rest The force on the cart due to the scale is parallel to the slope and in the upwards direction. The measurements show that this force is proportional to the height to which one end of the board is raised (or more properly, to the steepness H/D -- but D is not changing in this activity).
The cart is not moving, and so there is no net force on the cart. Gravity and the ramp are
also exerting forces on the cart, which combine to produce a force down the ramp, and of
the same size as the force the scale is exerting. If the cart were to slip from the hook on
the scale, there would be an unbalanced force and the cart would move down the plane.
Check the box when you are done: