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

1) 57 revolutions.

2) 4.52 m

3) 1531.2 m

Step-by-step 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}=(19.8)/(7)=2.83\ m/s^2`

Now, displacement of the tire is given as:

`S=ut+(a)/(2)t^2\\S=0+(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*(Diameter)=\pi * 38.5* 10^(-2)=1.2095\ m`

Now, number of revolutions is given as:

`N=(Total\ displacement)/(Displacement\ per\ revolution)\\N=(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* (\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.