Answer: F = 139.65 N
Explanation:
Using Pascal principle:
F = P * A, where
F = Force applied to the piston
P = Pressure
A = Piston area
also, we know generally,
A = πd²/4, in this case,
d= piston diameter
Calculation of the force Fp necessary to support the weight of the car.
Now, we use the Pascal principle: to solve,
Fp = P * Ap, where
Fp = Force on the primary piston
Ap = Primary piston area
we know our Ap but not P, so to find P
We use Newton's first law for a balanced Secondary piston -automobile system
Newton's first law: ∑F = 0
W - Fs = 0, where
W = car weight
Fs = Force on the secondary piston
Thus, W = Fs, if we put this in the equation, it becomes
W = P * As, where
As= Secondary piston area
making P subject of formula,
P = W / As
Substituting this in the initial equation, we have
Fp = W/As * Ap
From this, we know that
As = πds²/4
Ap = πdp²/4, so that
Fp = W/(πds²/4) * πdp²/4
Fp = 4W/πds² * πdp²/4
Fp = W/ds² * dp²
Fp = 2250/24.5² * 1.95²
Fp = 2250/600.25 * 3.8025
Fp = 14.25 kg
Converting to N, we have
14.25 * 9.8 = 139.65 N
