Question

A car is driving on a straight, level road at constant speed. Draw an FBD for the car, showing the significant forces that act upon it.

Short answer

Question: Draw a free body diagram for a car driving on a straight, level road at a constant speed and explain the forces acting upon it. Answer: To draw a free body diagram for a car driving on a straight, level road at a constant speed, we need to identify the significant forces acting upon the car. There are four main forces: gravitational force (W), normal force (N), frictional force (Fr), and traction force (T). The diagram should show these forces as vectors, with W and N being vertical forces and Fr and T being horizontal forces. The net force acting on the car is zero, allowing it to maintain its constant speed.

Step-by-step solution

Identifying the significant forces

There are four main forces acting on the car: 1. Gravitational force (Weight) - The force due to the Earth's gravity acting vertically downwards on the car. 2. Normal force - The force exerted by the road surface vertically upwards on the car to counterbalance the gravitational force. 3. Frictional force - The force acting opposite to the direction of motion, which prevents the car from sliding along the road surface. 4. Traction force - The driving force provided by the car's engine to ensure the car maintains its constant speed.

Set up coordinates

To set up the FBD, first, we need to choose a coordinate system for representing the forces. Since the car moves only horizontally, we can choose a 2D coordinate system with: - x-axis: horizontal direction (positive to the right) - y-axis: vertical direction (positive upwards)

Representing the forces in the FBD

Now, we will represent the identified forces as arrows in the FBD, pointing in their respective directions according to the chosen coordinate system. 1. Gravitational force (W): Draw a downward arrow from the center of mass of the car, to represent the vertical downward force acting on the car due to gravity. 2. Normal force (N): Draw an upward arrow from the point of contact between the car and the road surface to represent the force exerted by the road on the car. 3. Frictional force (Fr): Draw a horizontal arrow pointing in the direction opposite to the car's motion, to represent the friction between the road surface and the car's tires. 4. Traction force (T): Draw a horizontal arrow pointing in the direction of the car's motion from the point where the car's tires are in contact with the road surface.

Label the forces

Lastly, label each force vector with its respective symbol (W, N, Fr, T) and the angle at which it acts with respect to the coordinate system. Since W and N are vertically upward and downward, they are acting at 90° with respect to the x-axis. Fr and T forces are acting horizontally along the x-axis, so they have angles of 0° and 180° with respect to the x-axis. The free body diagram for the car driving on a straight, level road at a constant speed should now show all significant forces acting upon the car, with their respective magnitudes and directions. By analyzing this FBD, we can conclude that the forces acting on the car are balanced, resulting in a net force of zero, which allows it to maintain a constant speed.