How Does Raising One Wheel Affect Corner Weights in a Car?

In summary, when one wheel of a 3000lb car with a wheelbase of 100 inches and track of 50 inches is raised by 1 inch, the new equilibrium will result in varying corner weights depending on the distribution of weight on the other three wheels. The effective spring rate of 700 lb/in at each wheel may also play a factor in determining the new weights. To accurately calculate the new corner weights, a free body diagram and equations of statics may be used.
  • #1
aande
2
0

Homework Statement


A 3000lb car with a wheelbase of 100 inches and track of 50 inches sits on level ground with equal weight on each wheel. The effective spring rate is 700 lb/in at each wheel. One wheel is now raised by 1 inch and the car is allowed to settle to a new equilibrium. What is the new set of corner weights?

Homework Equations


F=k*x


The Attempt at a Solution


I tried solving this equation through reasoning and using Matlab. Obviously when the car is sitting on level ground the weight on each tire is 750lb. But as the left rear tire is raised I am unsure how to reason out what the new weight would be. I know the weight would increase on the front right and I think on the rear left. I'm not sure how to show this mathematically though.
 
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  • #2
Draw a free body diagram of the car. Since the car is in equilibrium with three wheels instead of four, the amount of weight on each wheel can be determined by writing and solving the equations of statics.
 
  • #3
The wheel is still in contact with a surface its just one inch higher than the rest. It's like the car is on a 1 inch block which is under one wheel.
 
  • #4
The car is still in equilibrium. There is an additional load at the lifted wheel due to the compression of the spring.
 
  • #5



The new set of corner weights can be calculated using the formula F=k*x, where F is the force, k is the effective spring rate, and x is the deflection. In this case, with a 1 inch deflection at one wheel, the new force on that wheel would be 700 lb (700 lb/in * 1 in). This would result in a redistribution of weight on the other three wheels, with the weight on the front right increasing by 175 lb (700 lb/in * 0.25 in) and the weight on the rear left increasing by 175 lb (700 lb/in * 0.25 in). The weight on the other wheel, front left, would remain the same at 750 lb. Therefore, the new set of corner weights would be 925 lb on the front right, 925 lb on the rear left, and 750 lb on the front left.
 

1. What is the relationship between spring rate and deflection?

Spring rate and deflection have an inverse relationship. This means that as the spring rate increases, the deflection decreases, and vice versa. In other words, a stiffer spring will require more force to compress it and will have less deflection compared to a softer spring.

2. How is spring rate measured?

Spring rate is typically measured in units of force per unit length, such as pounds per inch or Newtons per millimeter. It is calculated by dividing the force applied to the spring by the amount of deflection it produces.

3. What factors affect spring rate and deflection?

The main factors that affect spring rate and deflection include the material and geometry of the spring, the number of coils, and the initial tension or preload on the spring. The type of load applied to the spring, such as compression or tension, also plays a role.

4. How does temperature affect spring rate and deflection?

Temperature can have a significant impact on the spring rate and deflection. As temperature increases, the material of the spring may become softer and more pliable, resulting in a decrease in spring rate and an increase in deflection. Conversely, colder temperatures can make the spring stiffer and lead to a higher spring rate and less deflection.

5. What are some common applications of springs with different spring rates and deflections?

Springs with different spring rates and deflections are used in a variety of applications, such as in suspension systems for vehicles, shock absorbers, and mechanical watches. They are also commonly used in industrial machinery, medical devices, and household appliances.

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