Determining the Required Braking Force for a Vehicle on an Incline
In scenarios where vehicles are parked on inclines, it is crucial to understand the forces at play to ensure their stability. This article explains how to calculate the minimum braking force required to keep a specific vehicle stationary on an 18-degree incline, providing insights into the principles of physics and the practical applications in vehicle safety.
Key Concepts
The main concepts involved in this calculation include gravitational force, the angle of inclination, and the component of force parallel to the incline. By understanding these factors, we can ensure that vehicles remain safely in place and prevent any unwanted movement.
Mechanics of the Problem
Consider a vehicle with a mass of 1500 kg that is resting on an incline of 18° to the horizontal. The force of gravity acting on this vehicle can be broken down into two components: one perpendicular to the incline (normal force) and one parallel to the incline (which tends to cause the vehicle to slide down).
Calculating the Required Braking Force
To compute the required braking force, we need to calculate the component of the vehicle's weight (gravitational force) that is parallel to the incline. This can be done using the following steps:
Step 1: Determine the Gravitational Force
The gravitational force acting on the vehicle is given by:
[ F_{gravity} m times g ]
Where:
( m ) is the mass of the vehicle (1500 kg) ( g ) is the acceleration due to gravity (9.81 m/s2)So,
[ F_{gravity} 1500 text{ kg} times 9.81 text{ m/s}^2 14715 text{ N} ]
Step 2: Calculate the Component Parallel to the Incline
The component of the gravitational force parallel to the incline is given by:
[ F_{parallel} F_{gravity} times sin(theta) ]
Where:
( theta ) is the angle of the incline (18°)So,
[ F_{parallel} 14715 text{ N} times sin(18°) ]
[ F_{parallel} approx 4542.55 text{ N} ]
Step 3: Applying the Braking Force
For the vehicle to remain stationary, the braking force must be equal in magnitude but opposite in direction to the component of the gravitational force parallel to the incline. Therefore, the required braking force is:
[ F_{braking} 4542.55 text{ N} ]
This braking force must be applied upward along the incline to counteract the component of the gravitational force that tends to pull the vehicle downhill.
Conclusion
The minimum required braking force to keep a 1500 kg vehicle stationary on an incline of 18° is approximately 4542.55 N. Understanding and applying these principles ensures the safety of vehicles on inclines, thus preventing potential accidents.