Conceptual Physics Glenn Furnier Force Diagrams A force diagram is a useful tool for understanding the motion of an object. In a force diagram, one uses vectors to draw all the forces acting on an object. Adding these vectors will give the net force. If the net force is zero, the object will not accelerate because of inertia. If it is still, it will stay still. If it is moving, it will continue moving with a constant velocity. If the net force is not zero, the net force vector shows the direction and magnitude of the object’s acceleration. Your objective in this exercise is to be able to draw force diagrams. Figure 1 presents a force diagram for a car parked on a level surface. We can see that the force of gravity is exactly balanced by the support force. The net force is zero and the car does not accelerate, remaining parked. In Figure 2, the force of gravity and the support force are once again balanced. The force of the road pushing forward on the car (ultimately generated by the car’s motor) is perfectly balanced by the force of air resistance pushing back on the car. Adding all the force vectors in Figure 2, we obtain a net force of zero, meaning that the car does not accelerate, continuing along the highway at a constant velocity. support road pushes car air road pushes car
support
Fig. 1
Gravity
support air
Fig. 2
Gravity
Fig. 3
Gravity
Figure 3 shows the case in which the driver has pressed the gas pedal, providing more force from the engine and a greater push of the road onto the car in a forward direction. In this case, the forces are not completely balanced, resulting in a net force vector that is not zero and is pointed forward. Thus, the car accelerates forward. To slow down the car, we would reduce the pressure on the gas pedal or press the brake, so that the force of air resistance toward the back of the car is greater than the force of the road pushing forward on the car. This would result in negative acceleration, with the car slowing down. If the car is being driven on a highway at a constant speed and the driver wishes to turn left, she turns the steering wheel toward the left. This turns the tires toward the left. The actual force to accelerate the car by changing its direction is the force of friction between the tires and the road. Figure 4 shows this situation. From this perspective, we cannot see the perfectly balanced forces of the road pushing the car forward (into the paper) and the friction opposing the movement of the car (out of the paper). The result of adding these five vectors is a net force toward the left, accelerating the car toward the left.
support Friction
Fig. 4
gravity
friction
support
gravity Fig. 5
The situation becomes more complicated if the car is on a slope. Figure 5 shows a car that is parked on a slope. Gravity continues to pull toward the center of the earth, as always. The support force is perpendicular to the road surface, as always. To balance out these two forces, the force of friction must be oriented upslope. In this case, adding all three forces vectors we obtain a net force of zero, meaning that the car does not accelerate, remaining parked on the slope.
road pushes car support support
road pushes car
air Fig. 6
Gravity
air Fig. 7
Gravity
Figure 6 represents a car being driven upslope. The force vectors add up to a net force of zero, so the car does not accelerate, continuing to travel upslope at a constant velocity. Figure 7 shows the case in which the driver has pressed the gas pedal, providing more force from the engine and a greater push of the road onto the car in an upslope direction. In this case, the forces are not completely balanced, resulting in a net force vector that is not zero and is pointed upslope. Thus, the car accelerates upslope. To slow down the car, we would reduce the pressure on the gas pedal or press the brake, so that the force of the road pushing upslope on the car is less than the force of friction toward the back of the car (downslope) and the force of gravity. This would result in negative acceleration, with the car slowing down. As you can see, force diagrams allow one to see all the forces acting on an object. By seeing all the forces, one can determine the net force and predict whether the object will accelerate. If it does accelerate, the diagram allows us to predict the direction and magnitude of the acceleration. These diagrams are widely used by engineers and architects to understand the behavior of objects, such as bridges, ceilings, arches, and other structures. They are also used by geologists and meteorologists to understand the movements of our earth and its atmosphere.
Force Diagram Practice Problems For each of the following practice problems, please draw a force diagram. The diagram should include the object and vectors representing all the forces acting on it. Please also draw a vector showing the magnitude and direction of the net force. If the net force is zero, please write “net force = 0”. 1. A person stands still on the floor. Draw the forces on the person. 2. A person is standing on a slope. Draw the forces on the person. 3. A person is walking up a hill at a constant velocity. Draw the forces on the person. 4. A person is walking up a hill, but their speed is slowing down. Draw the forces on the person. 5. A ball is following a parabola through the air. Draw the forces on the ball. 6. A ball is falling freely straight down. Draw the forces on the ball. 7. A ball is rolling down a hill at a constant velocity. Draw the forces on the ball. 8. A ball is slowing down as it rolls down a hill. Draw the forces on the ball. 9. A cart is being pushed at a constant velocity across a floor. Draw the forces on the cart. 10. A cart is slowing down as it is pushed across a floor. Draw the forces on the cart.