Question
What is the free-body diagram of a car in a skid with its brakes locked up?
Answers
GPT-4o mini
To create a free-body diagram (FBD) for a car in a skid with its brakes locked up, we need to consider all the forces acting on the car. Here’s a breakdown of the forces typically involved:
1. **Weight (Gravity)**: This force acts downwards, equal to the mass of the car (m) times the acceleration due to gravity (g). It can be represented as \( F_g = mg \), pointing downward from the center of mass of the car.
2. **Normal Force**: This force acts upward, perpendicular to the surface on which the car is skidding. The normal force (N) balances the weight of the car in the vertical direction. In the absence of vertical acceleration, \( N = mg \).
3. **Frictional Force**: When a car is skidding (especially with locked brakes), the primary horizontal force acting on it is the kinetic friction force (F_f). This force acts opposite to the direction of motion, working to slow down the car. It is given by \( F_f = \mu_k N \), where \( \mu_k \) is the coefficient of kinetic friction.
4. **Drag Force (if applicable)**: If the car is moving through air, there would also be a drag force acting opposite to the direction of motion, but for simplicity, we can focus on the frictional force.
In the FBD, you would typically depict:
- An arrow pointing downwards for the weight of the car (mg).
- An arrow pointing upwards for the normal force (N), equal in magnitude to the weight.
- An arrow pointing horizontally opposite to the direction of the skid for the frictional force (F_f).
### Layout of the Free-Body Diagram:
- Draw a box or a car symbol in the center to represent the car.
- Draw an arrow pointing down from the center of the box indicating the gravitational force (label as \( F_g \)).
- Draw an arrow pointing up from the box of equal length indicating the normal force (label as \( N \)).
- Draw a horizontal arrow pointing opposite the direction of motion (skid direction) indicating the kinetic friction force (label as \( F_f \)).
This diagram helps to visualize the forces acting on the car and aids in further calculations regarding its motion, acceleration, and stopping distance during a skid.
1. **Weight (Gravity)**: This force acts downwards, equal to the mass of the car (m) times the acceleration due to gravity (g). It can be represented as \( F_g = mg \), pointing downward from the center of mass of the car.
2. **Normal Force**: This force acts upward, perpendicular to the surface on which the car is skidding. The normal force (N) balances the weight of the car in the vertical direction. In the absence of vertical acceleration, \( N = mg \).
3. **Frictional Force**: When a car is skidding (especially with locked brakes), the primary horizontal force acting on it is the kinetic friction force (F_f). This force acts opposite to the direction of motion, working to slow down the car. It is given by \( F_f = \mu_k N \), where \( \mu_k \) is the coefficient of kinetic friction.
4. **Drag Force (if applicable)**: If the car is moving through air, there would also be a drag force acting opposite to the direction of motion, but for simplicity, we can focus on the frictional force.
In the FBD, you would typically depict:
- An arrow pointing downwards for the weight of the car (mg).
- An arrow pointing upwards for the normal force (N), equal in magnitude to the weight.
- An arrow pointing horizontally opposite to the direction of the skid for the frictional force (F_f).
### Layout of the Free-Body Diagram:
- Draw a box or a car symbol in the center to represent the car.
- Draw an arrow pointing down from the center of the box indicating the gravitational force (label as \( F_g \)).
- Draw an arrow pointing up from the box of equal length indicating the normal force (label as \( N \)).
- Draw a horizontal arrow pointing opposite the direction of motion (skid direction) indicating the kinetic friction force (label as \( F_f \)).
This diagram helps to visualize the forces acting on the car and aids in further calculations regarding its motion, acceleration, and stopping distance during a skid.