Answer:
a. [tex]Area=144cm^{2}[/tex]
b. decrease
c. 43.5psi
Explanation:
Answer:
a. [tex]Area=144cm^{2}[/tex]
Explanation:
from the questions, the car has four tires which support the weight equally.we can conclude that the weight support by each tire is
weight support of each tire =1420/4=355kg.
a. since [tex]pressure=\frac{force}{area}[/tex]
we need to determine the force, [tex]F=mg\\[/tex]
the "g" is the acceleration due to gravity which has a constant value of [tex]9.8m/s^{2}[/tex]
hence the force on each tire is
[tex]F=mg\\F=355*9.8\\F=3479N\\[/tex]
Also, since the pressure is giving in psi, we have to convert it to pascal
since 1psi=6895pascal
hence 35psi to pascal is
[tex]35*6895\\241325pa[/tex].
From the expression for pressure
[tex]pressure =\frac{force}{area}\\[/tex]
we have
[tex]Area=\frac{force}{area}\\\\ Area=\frac{3479}{241325} \\Arae=0.0144\\[/tex]
to cm[tex]^{2}[/tex] we multiply by [tex]10^{4}[/tex]
[tex]Area=144cm^{2}[/tex]
b. The effect of the pressure can be determine from the relationship between the pressure and the area using the pressure formula
[tex]p=\frac{force}{area} \\p\alpha \frac{1}{A}\\[/tex]
hence an increase in the pressure will lead to a decrease in the contact Area
C. if the area ia now [tex]116cm^{2} \\[/tex] converting to meter square
[tex]116/10^{4} \\Area=0.0116m^{2} \\[/tex]
the pressure now is
[tex]pressure=\frac{force}{area} \\Pressur=\frac{3479}{0.0116}\\ pressure=299913.8pa\\[/tex]
converting to psi we have
[tex]299913.8/6895\\pressure=43.5psi[/tex]
(a) The area of contact of each tire is 114.17 cm².
(b) If the gauge pressure increases, the contact area decreases.
(c) The necessary gauge pressure in the tires is 43.5 psi.
The area of contact of each tire is calculated as follows;
P = F/A
A = F/P
where;
Weight of each tire, W = mg/4 = (1420 x 9.8)/4 = 3479 N
Pressure of each tire = 35 psi = 241,317 Pa
A = W/P
A = 3479/241317
A = 0.014417 m²
A = 144.17 cm²
If the gauge pressure increases, the contact area decreases.
When the contact area is 116 cm² = 0.0116 m², the gauge pressure of each tire is calculated as follows;
P = W/A
P = 3479/0.0116
P = 299,913.8 Pa
convert to psi by dividing with 6895
P = 43.5 psi
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