Share
A car of mass 410 kg travels around a flat, circular race track of radius 83.4 m. The coefficient of static friction between the wheels and
Question
A car of mass 410 kg travels around a flat, circular race track of radius 83.4 m. The coefficient of static friction between the wheels and the track is 0.286. The acceleration of gravity is 9.8 m/s 2 . What is the maximum speed v that the car can go without flying off the track
in progress
0
Physics
3 years
2021-08-26T08:38:42+00:00
2021-08-26T08:38:42+00:00 1 Answers
114 views
0
Answers ( )
Answer:
The maximum speed v that the car can go without flying off the track = 15.29 m/s
Explanation:
let us first lay out the information clearly:
mass of car (m) = 410 kg
radius of race track (r) = 83.4 m
coefficient of friction (μ) = 0.286
acceleration due to gravity (g) = 9.8 m/s²
maximum speed = v m/s
For a body in a constant circular motion, the centripetal for (F) acting on the body is given by:
F = mass × ω
where:
F = maximum centripetal force = mass × μ × g
ω = angular acceleration =![Rendered by QuickLaTeX.com \frac{(velocity)^2}{radius}](https://documen.tv/wp-content/ql-cache/quicklatex.com-f8c858a0148f902e72bb4938093e2be4_l3.png)
∴ F = mass × ω
m × μ × g = m ×![Rendered by QuickLaTeX.com \frac{v^{2} }{r}](https://documen.tv/wp-content/ql-cache/quicklatex.com-f52dd8c3fb0b7b0f4183e6225a30d42b_l3.png)
410 × 0.286 × 9.8 = 410 ×![Rendered by QuickLaTeX.com \frac{v^{2} }{83.4}](https://documen.tv/wp-content/ql-cache/quicklatex.com-bc24b65b910294662634b0cf5742ab92_l3.png)
since 410 is on both sides, they will cancel out:
0.286 × 9.8 =![Rendered by QuickLaTeX.com \frac{v^{2} }{83.4}](https://documen.tv/wp-content/ql-cache/quicklatex.com-bc24b65b910294662634b0cf5742ab92_l3.png)
2.8028 =![Rendered by QuickLaTeX.com \frac{v^{2} }{83.4}](https://documen.tv/wp-content/ql-cache/quicklatex.com-bc24b65b910294662634b0cf5742ab92_l3.png)
now, we cross-multiply the equation
2.8028 × 83.4 =![Rendered by QuickLaTeX.com v^{2}](https://documen.tv/wp-content/ql-cache/quicklatex.com-427e63ea66e8d216289eae37ca61780a_l3.png)
∴ v = √(233.754)
v = 15.29 m/s
Therefore, the maximum speed v that the car can go without flying off the track = 15.29 m/s