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
Andre45 [30]
3 years ago
11

An ant sits on a cd at a distance of 17 cm from the centre. If it sits there for 42 seconds, it travels a total distance of 913

cm. a. What angle has the ant turned through? (in radians) b. What speed has the ant been traveling at? (in cm/sec) c. What angular velocity has the ant been spinning at? (in radians/sec) d. What rpm is the cd turning at?
Physics
1 answer:
lys-0071 [83]3 years ago
4 0

a) 53.7 rad

b) 21.7 cm/s

c) 1.28 rad/s

d) 12.2 rpm

Explanation:

a)

The ant sits on the cd at a distance of

r = 17 cm

from the centre: this is therefore the radius of the circle covered by the ant.

Therefore, we can find the length of the circumference of the circle:

c=2\pi r=2\pi(17)=106.8 cm

A full circle corresponds to an angle of

\theta = 2\pi rad

In this problem instead, the distance covered by the ant along the circle is

d = 913 cm

Therefore, the angle corresponding to this distance can be found by using the rule of three:

\frac{\theta}{c}=\frac{\theta'}{d}

And so we find:

\theta'=\theta \frac{d}{c}=(2\pi)\frac{913}{106.8}=53.7 rad

b)

The speed of the ant can be calculated by using

v=\frac{d}{t}

where

d is the distance travelled by the ant

t is the time taken to cover that distance

v is the speed

In this problem:

d = 913 cm is the distance covered by the ant

t = 42 s is the time elapsed

Therefore, the speed of the ant is:

v=\frac{913}{42}=21.7 cm/s

c)

The angular velocity of an object in rotation is the rate of change of the angular displacement.

The angular velocity is related to the linear speed by

\omega=\frac{v}{r}

where

\omega is the angular velocity

v is the linear speed

r is the radius of the circle

In this problem:

v = 21.7 cm/s is the speed of the ant

r = 17 cm is the radius of the circle

So, the angular velocity of the ant is:

\omega=\frac{21.7}{17}=1.28 rad/s

d)

The rpm means "revolutions per minute", and it is another units used to express the angular velocity.

In order to convert the angular velocity from radians per second to rmp, we must keep in mind that:

1 revolution = 2\pi radians

1 minute = 60 seconds

The angular velocity of the ant in this problem is

\omega=1.28 rad/s

Therefore, in order to convert to rpm, we apply the two conversion factors above, and so we get:

\omega = 1.28 \frac{rad}{s}\cdot \frac{60 s/min}{2\pi rad/rev}=12.2 rev/min

So, the cd is turning at 12.2 rpm.

You might be interested in
A plane wave has equation; y= 25sin(120 _4x).find the: (1)wave length (2)wave velocity (3)frequency and period of the wave
kupik [55]

(1) The wavelength of the wave is 1.57 m.

(2) The velocity of the wave is 30 m/s .

(3) The frequency of the wave is 19.10 Hz and the time period of the    wave is 0.052 s.

Note: The given equation seems to be incomplete. Most probably the equation was y=25sin(120t-4x). And the standard system of units (i.e. kg, m, s) is used.

Wavelength: The distance between the consecutive crest or trough of a wave is called the wavelength of a wave.

The equation of a plane wave oscillating in the y direction and traveling in the x direction is given by the equation,

y=A sin(ωt-kx)

where y is the displacement along the y direction, A is the amplitude of the wave, ω is the angular frequency, t is the time, x is the displacement along the x direction, and k is the wave constant.

The given equation is,

y=25sin(120t-4x)

Comparing this equation with the above equation, following values are obtained.

k= 4 m^(-1)

ω =120 rad/s

A=25

The wavelength λ is given by the formula,

λ=2π/k

Here k = 4 m^(-1), so

λ=2π/4

λ=1.57 m.

Velocity: The velocity of a wave is the product of the frequency and the wavelength.

The velocity v is given by the formula,

v=ω*λ/2π

Here ω=120 rad/s and λ=1.57 m, so

v=120*1.57/2π

v=30 m/s

Frequency: The number of oscillations completed in one second is called the frequency of a wave.

The formula of the frequency is,

f=v/λ

Here v=30 m/s and λ=1.57 m, so

f=30/1.57

f=19.10 Hz

Time period: The time taken to complete one cycle of oscillation is called the time period of oscillation.

The formula to calculate the time period T is,

T=2π/ω

Here ω=120 rad/s, so

T=2π/120

T=0.052 s.

Learn more about velocity of wave.

brainly.com/question/25847786

#SPJ4

8 0
2 years ago
A mass of 3.0 kg rests on a smooth surface inclined 34° above the horizontal. It is kept from sliding down the plane by a spring
azamat

Answer:

The spring stretched by x = 13.7 cm

Explanation:

Given data

Mass = 3 kg

k = 120 \frac{N}{m}

Angle \theta = 34°

From the free body diagram

Force acting on the box = mg sin\theta

⇒ F = 3 × 9.81 × \sin34

⇒ F = 16.45 N ------- (1)

Since box is attached with the spring so a spring force also acts on the box.

F_{sp} = k x

F_{sp} = 120 x -------- (2)

The net force acting on the body is given by

F_{net} = ma

Since acceleration of the box is zero so

F_{net} = 0

F - F_{sp} = 0

F = F_{sp}

Put the values from equation (1) & (2) we get

16.45 = 120x

x = 0.137 m

x = 13.7 cm

Therefore the spring stretched by x = 13.7 cm

3 0
3 years ago
1. °C= (°F-32) X 5/9. what will be the answer?
aleksley [76]

Answer:

F=9/5(°C)+32

Explanation:

Lets take an example

  • Take 25°C

\\ \sf\longmapsto \dfrac{9}{5}(25)+32

\\ \sf\longmapsto 9(5)+32

\\ \sf\longmapsto 45+32

\\ \sf\longmapsto 77°F

3 0
3 years ago
True or false. Students with a Learners License may not receive a motorcycle endorsement.
viktelen [127]
This is a true statement 
3 0
3 years ago
How can an individual benefit from participating in the recommended amount of physical activity?
Orlov [11]
It will help them stay in better shape resulting in better health, being more physically active, and staying happier as a result.
3 0
3 years ago
Other questions:
  • Looking at the periodic table which element would you think is the best conductor of electricity?
    12·1 answer
  • If it took 10sec to climb the ladder what was your power in watts nd kilowatt?
    7·1 answer
  • Devon places sliced potatoes in a package of aluminum foil. He puts a metal grate over a campfire and sets the package on the gr
    11·2 answers
  • A snail crawls along at a constant rate of 3 centimeters per minute in a northly direction. This is a description of the snails
    14·2 answers
  • Select the statement that correctly completes the description of phase difference.
    5·1 answer
  • Bethany had a beaker with a small amount of baking soda. She added a few drops of pickle juice to the baking soda and observed f
    12·2 answers
  • All BUT one is a function of the cell wall. That is___
    13·1 answer
  • the electric charge remains at rest in a. static electricity, b. current electricity, c. none of these​
    14·1 answer
  • What is the efficiency of a ramp if the input work is 96 J and the output work is 24 J?
    11·1 answer
  • Every winter i fly home to Michigan. it takes 5 hours. what is my average speed?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!