Physics, 26.10.2020 17:30, natethawsm

A cyclist uses a stationary trainer during the winter to keep in shape. Knowing that she pushes down on her pedal with a velocity of 26 in./s that increases at a rate of 2.2 in./s2, determine the velocity and acceleration (tangential and normal) of point D on the bottom of the rear wheel.

Answers: 2

Show answers

Answers

answered: genyjoannerubiera

v = 112in/s

a = 896.05in/s²

Explanation: Angular velocity is the arc traveled per change in time or:

$\omega=\frac{v}{r}$

For the pedal, it will be:

$\omega_{p}=\frac{v_{p}}{r_{p}}$

$\omega_{p}=\frac{26}{6.5}$

$\omega_{p}=4$ rad/s

Angular velocity of the pedal is equal to the angular velocity of the chain:

$\omega_{p}d_{p}=\omega_{s}d_{s}$

where

$d_{p}$ is diameter of the pedal

$d_{s}$ is diameter of the small circle at the rear wheel

$\omega_{s}=\frac{7}{3.5}.4$

$\omega_{s}$ = 8 rad/s

Velocity at the point D at the bottom othe rear wheel:

$v_{D}=\omega_{s}r_{D}$

$v_{D}=$ 8.14

$v_{D}$ = 112in/s

Velocity at point D is 112 in/s.

Acceleration in circular motion is the vectorial sum of normal and tangential acceleration.

Angular acceleration is also known as centripetal acceleration, due to its direction pointing towards the center. It is "responsible" for changing the object direction. It is calculated as $a_{c}=\omega^{2}.r$

Tangential acceleration is the change in magnitude of the circular motion and is calculated as

$a_{t}=r.\frac{\Delta \omega}{\Delta t}$ or $a_{t}=r.\alpha$

Angular and tangential accelerations are directly proportional.

Tangential Acceleration of the pedal is:

$\alpha_{p}=\frac{a_{t}}{r}$

$\alpha_{p}=\frac{2.2}{6.5}$

$\alpha_{p}$ = 0.34 rad/s²

Tangential acceleration at the pedal is equal to angular acceleration at the rear wheel:

$r_{w}.\alpha_{w}=r_{p}.\alpha_{p}$

$r_{w}$ is radius of the small circle at the rear wheel

$r_{p}$ is radius of the pedal

$\alpha_{w}=\frac{3.5}{1.75}.0.34$

$\alpha_{w}$ = 0.68 rad/s²

At the point D, tangential acceleration will be:

$a_{t,D}=\alpha_{w}.r_{D}$

$a_{t,D}=0.68*14$

$a_{td,D}$ = 9.52 in/s²

Centripetal acceleration at point D is:

$a_{c,D}=\omega_{D}^{2}.r_{D}$

$a_{c,D}=8^{2}.14$

$a_{c,D}$ = 896 in/s²

Net acceleration:

$a_{D}=\sqrt{a_{t,D}^{2}+a_{c,D}^{2}}$

$a_{D}=\sqrt{9.52^{2}+896^{2}}$

$a_{D}$ = 896.05 in/s²

Acceleration of point D at the bottom of rear wheel is 896.05 in/s²

A cyclist uses a stationary trainer during the winter to keep in shape. Knowing that she pushes down

answered: Guest

Ibelieve the correct answer would be c.

answered: Guest

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

$p(t)=0.3t^2+6t+80$

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

$p(0)=0+0+80=80$

according to question, we have said that if the population has twice its initial population, then it becomes

$p(t)=2\times 80=160$

so, time taken to reach this above mentioned population is given by

$160=0.3t^2+6t+80\\\\160-80=0.3t^2+6t\\\\80=0.3t^2+6t\\\\0.3t^2+6t-80=0\\\\\text{using quadratic formula ,we get }\\\\t_{1,\: 2}=\frac{-60\pm \sqrt{60^2-4\cdot \: 3\cdot \: 800}}{2\cdot \: 3}\\\\t=-29.14\ and\ t=9.149$

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.

Other questions on the subject: Physics

Physics, 21.06.2019 23:00, laurachealsy923

How many dots must be added to the symbol to properly represent a standard nitrogen ion? a) 1 b) 3 c) 5 d) 8

Answers: 1

continue

Physics, 22.06.2019 08:00, Savageboyn

Gather reliable information to brent make his decision. to gather this information, use newspapers, call insurance companies or look at their web sites, and review consumer magazines and web sites. also, look at the manufacturer web site or for information about gas mileage. list the sources you use and take notes.

Answers: 1

continue

Physics, 22.06.2019 16:00, AriaMartinez

Fill in the blanks with the numbers is a measure of the resistance to flow. a high liquid has a high resistance to flow and flows slowly. the ancients thought everything in the world was made of 4 we now know that there are 94 naturally occurring and scientists have created another 24 i am certain they will create even more. honey flows slowly because it has a high to flowing. a can be separated by physical means because it contains more than one pure substance and 2 pure substances are not chemically bonded to each other. a cannot be separated by physical means. all matter is made up of all elements are with the same number of protons. if it is just a single or many bonded together, if all of them have the same number of protons, it is an element. in a piece of pure iron metal, all the are joined together, that piece of iron metal is called elemental iron. a single of iron is called elemental iron. a mixture has differences from place to place. we might need a microscope to see them or they might be obvious to the unaided eye. there are surfaces separating it into different phases. a mixture is the same everywhere. it is uniform. there are no surfaces separating it into different phases. if different kinds of atoms (different elements) are bonded together by their electrons, it is called a there are physical means of to isolate the different pure substances in a mixture and there are chemical means of to isolate the different elements in a compound. 1. element 2. compound 3. mixture 4. heterogeneous 5. homogeneous 6. pure substance 7. atoms 8. separation 9. viscosity 10. resistance

Answers: 3

continue

Physics, 22.06.2019 22:00, saucyyyyniahhhhh

Four friends, a, b, c, and d are standing varying distances away from a speaker which is producing sound waves.

Answers: 2

continue

Do you know the correct answer?

A cyclist uses a stationary trainer during the winter to keep in shape. Knowing that she pushes down...