Question

1) A car accelerates uniformly from rest and reaches a speed of 19.8 m/s in 7 s. The diameter of a tire is 38.5 cm. Find the number of revolutions the tire makes during this motion, assuming no slipping.Answer in units of rev.
2) A wheel has a radius of 4.8 m.How far (path length) does a point on thecircumference travel if the wheel is rotatedthrough an angle of 54◦? Answer in units of m.

3) How far (path length) does a point on thecircumference travel if the wheel is rotatedthrough an angle of 319 rad?Answer in units of m

Answer 1

Answer:

1) 57 revolutions.

2) 4.52 m

3) 1531.2 m

Explanation:

Question 1:

Given:

Initial velocity, $u = 0$

Final velocity, $v = 19.8\ m/s$

Time, $t = 7\ s$

Acceleration, $a = \frac{\textrm{Final velocity-Initial velocity}}{Time}=\frac{19.8}{7}=2.83\ m/s^2$

Now, displacement of the tire is given as:

$S=ut+\frac{a}{2}t^2\\S=0+\frac{2.83}{2}7^2=69.335\ m$

Displacement of tire in 1 revolution is equal to its circumference.

Therefore, displacement in 1 revolution = $\pi\times(Diameter)=\pi \times 38.5\times 10^{-2}=1.2095\ m$

Now, number of revolutions is given as:

$N=\frac{Total\ displacement}{Displacement\ per\ revolution}\\N=\frac{69.335}{1.2095}=57$

Therefore, the number of revolutions are 57.

Question 2:

Given:

Radius of the wheel is, $R=4.8\ m$

Angle of rotation is, $\theta=54$°

Converting degree to radians, we get:

$\theta=54\times \frac{\pi}{180}=0.3\pi$

Now, path length is given as:

$L=R\theta=(4.8)(0.3\pi)=1531.2\ m$

Therefore, the path length of a point on the wheel is 4.52 m

Question 3:

Radius of the wheel is, $R=4.8\ m$

Angle of rotation is, $\theta=319$ radians

Now, path length is given as:

$L=R\theta=(4.8)(319)=4.52\ m$

Therefore, the path length of a point on the wheel is 1531.2 m.