contestada

A bicyclist starting at rest produces a constant angular acceleration of 1.30 rad/s2 for wheels that are 35.5 cm in radius.

(a) What is the bicycle's linear acceleration (in m/s2)?
(b) What is the angular speed of the wheels (in rad/s) when the bicyclist reaches 11.2 m/s?
(c) How many radians have the wheels turned through in that time?
(d) How far (in m) has the bicycle traveled?

Respuesta :

krlosdark12

Answer:

a) 0.462 m/s^2

b) 31.5 rad/s

c) 381 rad

d) 135m

Explanation:

the linear acceleration is given by:

[tex]a=\alpha *r\\a=1.30rad/s^2*(35.5*10^{-2}m)\\a=0.462m/s^2[/tex]

the angular speed is given by:

[tex]\omega=\frac{v}{r}\\\\\omega=\frac{11.2m/s}{35.5*10^{-2}m}\\\\\omega=31.5rad/s[/tex]

to calculate how many radians have the wheel turned we need the apply the following formula:

[tex]\theta=\frac{1}{2}\alpha*t^2\\\\t=\frac{\omega}{\alpha}\\\\t=\frac{31.5rad/s}{1.30rad/s^2}\\\\t=24.2s\\\\\theta=\frac{1}{2}*1.30rad/s^2*(24.2s)^2\\\\\theta=381rad[/tex]

the distance is given by:

[tex]d=\theta*r[/tex]

[tex]d=381rad*(35.5*10^{-2}m)\\d=135m[/tex]

Lanuel

a. The bicycle's linear acceleration (in [tex]m/s^2[/tex]) is 0.4615  [tex]m/s^2[/tex]

b. The angular speed of the wheels (in rad/s) when the bicyclist reaches 11.2 m/s is 31.55 rad/s.

c. The number of radians the wheels have turned through in that time is 382.87 rads.

d. The distance (in meters) the bicycle has traveled is 135.92 meters.

Given the following data:

  • Initial angular velocity = 0 rad/s (since the bicycle is at rest).
  • Angular acceleration = 1.30 [tex]rad/s^2[/tex]
  • Radius = 35.5 cm to m = 0.355 meters

a. To find the bicycle's linear acceleration (in [tex]m/s^2[/tex]):

Mathematically, linear acceleration is given by the formula:

[tex]Linear\;acceleration = \alpha r\\\\Linear\;acceleration = 1.30(0.355)[/tex]

Linear acceleration = 0.4615  [tex]m/s^2[/tex]

b. To find the angular speed of the wheels (in rad/s) when the bicyclist reaches 11.2 m/s:

Mathematically, angular speed is given by the formula:

[tex]Angular \;speed = \frac{Linear\;speed}{radius}\\\\Angular \;speed = \frac{11.2}{0.355}[/tex]

Angular speed = 31.55 rad/s

c. To find how many radians the wheels have turned through in that time:

First of all, we would determine the time by using the first equation of motion.

[tex]V = U + at\\\\11.2 = 0 + 0.4615t\\\\t = \frac{11.2}{0.4615}[/tex]

t = 24.27 seconds

[tex]\Theta = \frac{1}{2} \alpha t^2\\\\\Theta = \frac{1}{2} (1.30) (24.27^2)\\\\\Theta = 0.65(589.0329)[/tex]

Ф = 382.87 rads

d. To find how far (in meters) the bicycle has traveled:

[tex]Distance = r \theta\\\\Distance = 0.355(382.87)[/tex]

Distance = 135.92 meters.

Read more: https://brainly.com/question/14703849

Otras preguntas