To calculate the weight of the car using the given information, follow these steps:
1. Understand the Hydraulic Principle: According to Pascal's principle in hydraulics, the force applied on one piston creates an equal increase in pressure throughout the fluid. This increase in pressure translates to a proportional force on the second piston. If the area of the second piston is larger, the force exerted on it is proportionately larger.
2. Given Data:
- The area of the piston carrying the car (larger piston) is 50 times more than the area of the smaller piston.
- A force of 500 N is being applied to the smaller piston.
3. Relationship Between Forces and Areas: The force on the larger piston [tex]\(F_L\)[/tex] can be found using the ratio of the areas of the pistons. Since the larger piston has 50 times the area of the smaller piston:
[tex]\[
\text{Area Ratio} = \frac{\text{Area of Larger Piston}}{\text{Area of Smaller Piston}} = 50
\][/tex]
4. Calculating the Weight of the Car: Let [tex]\(F_S\)[/tex] be the force applied on the smaller piston, and in this case, [tex]\(F_S = 500 \, \text{N}\)[/tex]. The force on the larger piston, which corresponds to the weight of the car (W), can be calculated as follows:
[tex]\[
\text{Weight of the Car (W)} = \text{Area Ratio} \times F_S
\][/tex]
5. Substitution:
[tex]\[
W = 50 \times 500 \, \text{N}
\][/tex]
6. Final Calculation:
[tex]\[
W = 25000 \, \text{N}
\][/tex]
Therefore, the weight of the car is 25,000 Newtons.
