1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bearhunter [10]
3 years ago
12

A person is riding a bicycle, and its wheels have an angular velocity of 10.7 rad/s. Then, the brakes are applied and the bike i

s brought to a uniform stop. During braking, the angular displacement of each wheel is 19.5 revolutions.
(a) How much time does it take for the bike to come to rest?
(b) What is the anguar acceleration (in rad/s2) of each wheel?
Physics
1 answer:
Scilla [17]3 years ago
3 0

Answer:

(a) t = 22.9 s

(b) α= - 0.467 rad/s²

Explanation:

The uniformly accelerated circular movement, is a circular path movement in which the angular acceleration is constant.

We apply the equations of circular motion uniformly accelerated :

ωf ²=  ω₀² + 2*α*θ  Formula (1)

ωf= ω₀ + α*t Formula (2)

Where:

θ : angle that the body has rotated in a given time interval (rad)

α : angular acceleration (rad/s²)

t : time interval (s)

ω₀ : initial angular speed ( rad/s)

ωf : final angular speed ( rad/s)

Data

θ =  19.5 revolutions  : angular displacement of each wheel or angle that the  wheel has rotated in a given time interval

ω₀= 10.7 rad/s :  initial angular speed of the Wheel ( rad/s)

ωf = 0 : final angular speed  of the Whee( rad/s)

Calculating of the angular acceleration (α )

We replace data in the fómula (1),considering that 1 revolution is equal to 2π radians :

ωf ²=  ω₀² + 2*α*θ

(0 )²=  (10.7)² + 2*α*(19.5*2*π )

0= 114.49 + (245.04)*α

-114.49 =  (245.04)*α

α= (-114.49) /(245.04)

α= -114.49 /(245.04)

α= -0.467 rad/s²

Time does it take for the bike to come to rest

We replace data in the formula (2)

ωf = ω₀ + α*t

0 =  10.7 + -0.467*t

-10.7  = - 0.467*t    we multiply by (-1) both sides of the equation :

10.7  = 0.467*t  

t = 10.7 / 0.467

t = 22.9 s

You might be interested in
Scientific notation: Convert 7.1 x 10-3 to decimal notation.​
marysya [2.9K]

Answer: hey

your answer is gonna be

71000.

Explanation:

5 0
3 years ago
Suppose we consider the system of the three capacitors as a single "equivalent" capacitor. Given the charges of the three indivi
emmainna [20.7K]

Answer:

??????????????????????????????????????????????????????????????????

Explanation:

?????????????????????????????????????????????????

8 0
3 years ago
What is the force of a lead ball that starts with a momentum of 7 kg*m/s and end with a momentum of 22 kg*m/s over a time of 31
Gwar [14]

Answer:

F = 0.483 N

Explanation:

Initial momentum, P_i= 7\ kg-m/s

Final momentum, P_f= 22\ kg-m/s

Time, t = 31 s

We need to find the force of a lead ball. We can use here the impulse momentum theorem.

\text{Change in momentum}=F\times t

F is force

P_f-P_i=Ft\\\\F=\dfrac{P_f-P_i}{t}\\\\F=\dfrac{22-7}{31}\\\\F=0.483\ N

So, the force is 0.483 N.

6 0
3 years ago
The position of a particle s given by x=3-2t+3t^2. What is its instantaneous velocity and instantaneous acceleration as t=3.
Leno4ka [110]

Explanation:

velocity = dx/dt

\frac{dx}{dt}  = 6t - 2 = 16

acceleration =

\frac{ {d}^{2}x }{d {t}^{2} }  = 6 \ \\

5 0
2 years ago
A mass spectrometer was used in the discovery of the electron. In the velocity selector, the electric and magnetic fields are se
Mama L [17]

Answer:

Explanation:

Radius of dee, r = 8 mm = 0.008 m

Electric field, e = 400 V/m

Magnetic field, B = 4.7 x 10^-4 T

mass of electron, m = 9.1 x 10^-31 kg

charge of electron, q = 1.6 x 10^-19 C

(a) Let v is the speed of electrons.

v = \frac{Bqr}{m}

v = \frac{4.7\times 10^{-4}\times 1.6\times 10^{-19}\times 0.008}{9.1 \times 10^{-31}}

v = 661098.9 = 661099 m/s

(b)

\frac{e}{m}=\frac{1.6 \times 10^{-19}}{9.1\times 10^{-31}}

e / m = 1.76 x 10^14 C / kg

(c) Let K be the kinetic energy

K = 0.5 x mv²

K = 0.5 x 9.1 x 10^-31 x 661099 x 661099

K = 1.99 x 10^-19 J

K = 1.24 eV

So, the potential difference is

V = 1.24 V

(d) if the acceleration voltage is doubled

V = 2 x 1.24 = 2.48 V

So, Kinetic energy

K = 2.48 eV

K = 2.48 x 1.6 x 10^-19 = 3.968 x 10^-19 J

Let v is the speed

K = 0.5 x mv²

3.968 x 10^-19 = 0.5 x 9.1 x 10^-31 x v²

v = 933856.5 m/s

Let the new radius is r.

r=\frac{mv}{Bq}

r=\frac{9.1\times 10^{-31}\times 933856.5}{4.7\times 10^{-4}\times 1.6\times 10^{-19}}

r = 0.0113 m = 1.13 cm

7 0
3 years ago
Other questions:
  • “A 39.2 N object is pushed with 12 N of force but experiences 3 N of frictionWhat is the object's acceleration?”
    9·1 answer
  • 1) A uniform wooden beam, with mass of 120 and length L = 4 m, is supported as illustrated in the figure. If the static friction
    6·1 answer
  • Why can't passenger planes fly very high?
    13·2 answers
  • Which of the following correctly shows the four most abundant gases in the Earth's atmosphere in order from most abundant to lea
    14·2 answers
  • Which of the following is an example of acceleration? Select one:
    8·1 answer
  • An electrician is creating a wiring plan for a small house. He needs to create a plan that will allow the homeowners to turn off
    8·2 answers
  • A uniform magnetic field is perpendicular to the plane of a wire loop. If the loop accelerates in the direction of the field, wi
    5·1 answer
  • How much energy (in kW-h) does a 900 Watt stove use in a week if it is used for 1.5 hours each day?
    9·1 answer
  • An ant on a picnic table travels 7.3 cm eastward, then 7.5 cm northward. What is the magnitude of the ant's displacement relativ
    10·1 answer
  • if a person can jump 2m in earth surface how high can he jump in the moon (g of moon = 1.66m/s, g of earth = 9.8 m/s) [hint: use
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!