In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force of 49 N to the input piston, which has a radius r1. As a result, the output plunger, which has a radius r2, applies a force to the car. The ratio r2/r1 has a value of 6.9. Ignore the height difference between the input piston and output plunger and determine the force that the output plunger applies to the car.
there is a hint for this problem it is to use the equation P=F/A, but that doesn't make sense.
The pressure on each pistion is the same, so the force on each piston =Pressure*area.
So the area becomes significant in transmitting force. Force transmitted will be proportional to (A2/A2) which in turn is proportional to (r2/r1)^2
I am not getting it so what am I suppose to do. Is my equation correct.
Force2=force2(r2/r1)^2 Use that.
49Nx(6.9)^2= 2.3x10^3
Well, your equation is on the right track, but there seems to be a small typo. The correct equation should be:
Force2 = Force1 * (r2/r1)^2
Where Force1 is the force applied to the input piston (which is 49 N in this case), and r2/r1 is the ratio of the radii.
Now let's plug in the values:
Force2 = 49 N * (6.9)^2
That should give you the force that the output plunger applies to the car. Good luck with your tire change! And remember, if all else fails, call in a professional clown car service. They'll bring a whole team of clowns to fix it in no time!
Yes, your equation is correct. The correct equation to use in this situation is
Force2 = Force1 * (r2/r1)^2
where Force1 is the force applied to the input piston (49 N in this case), r1 is the radius of the input piston, r2 is the radius of the output plunger, and Force2 is the force applied by the output plunger to the car.
To solve the problem, substitute the given values into the equation. The given ratio of r2/r1 is 6.9. Let's assume the radius of the input piston (r1) is 1.
Force2 = 49 * (6.9/1)^2
Force2 = 49 * 6.9^2
Force2 ≈ 49 * 47.61
Force2 ≈ 2340.89 N
Therefore, the force that the output plunger applies to the car is approximately 2340.89 N.
Yes, your equation is correct. You can use the equation Force2 = Force1 * (r2/r1)^2 to determine the force that the output plunger applies to the car.
Here's how you can use the equation to solve the problem:
1. The input force (Force1) applied on the input piston is given as 49 N.
2. The ratio of the radii, r2/r1, is given as 6.9.
3. Plug these values into the equation and solve for Force2.
Force2 = 49 N * (6.9)^2
Force2 = 49 N * 47.61
Force2 ≈ 2372.89 N
Therefore, the force that the output plunger applies to the car is approximately 2372.89 N.
Remember, the equation P = F/A (pressure equals force divided by area) is also involved in understanding this problem. Pressure is the same on both pistons since they are connected through a hydraulic system. The force transmitted through the hydraulic system is proportional to the ratio of the areas, (r2/r1)^2. That's why you can use the equation Force2 = Force1 * (r2/r1)^2 to solve the problem.