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
yarga [219]
3 years ago
10

A 0.29 kg particle moves in an xy plane according to x(t) = - 19 + 1 t - 3 t3 and y(t) = 20 + 7 t - 9 t2, with x and y in meters

and t in seconds. At t = 1.1 s, what are (a) the magnitude and (b) the angle (within (-180°, 180°] interval relative to the positive direction of the x axis) of the net force on the particle, and (c) what is the angle of the particle's direction of travel?
Physics
1 answer:
Artist 52 [7]3 years ago
7 0

Answer:

Part a)

F = 7.76 N

Part b)

\theta = -137.7 degree

Part c)

\theta = -127.7 degree

Explanation:

As we know that acceleration is rate of change in velocity of the object

So here we know that

x = -19 + t - 3t^3

y = 20 + 7t - 9t^2

Part a)

differentiate x and y two times with respect to time to find the acceleration

a_x = \frac{d^2}{dt^2}(-19 + t - 3t^3)

a_x = \frac{d}{dt}(0 +1 - 9t^2)

a_x = -18t

a_y = \frac{d^2}{dt^2}(20 + 7t - 9t^2)

a_y = \frac{d}{dt}(0 +7 - 18t)

a_y = -18

Now the acceleration of the object is given as

\vec a = (-18t)\hat i + (-18)\hat j

at t= 1.1 s we have

\vec a = -19.8 \hat i - 18 \hat j

now the net force of the object is given as

\vec F = m\vec a

\vec F = (0.29 kg)(-19.8 \hat i - 18 \hat j)

\vec F = -5.74 \hat i - 5.22 \hat j

now magnitude of the force will be

F = \sqrt{5.74^2 + 5.22^2} = 7.76 N

Part b)

Direction of the force is given as

tan\theta = \frac{F_y}{F_x}

tan\theta = \frac{-5.22}{-5.74}

\theta = -137.7 degree

Part c)

For velocity of the particle we have

v_x = \frac{dx}[dt}

v_x = (0 +1 - 9t^2)

v_y = \frac{dy}{dt}

v_y = (0 +7 - 18t)

now at t = 1.1 s

\vec v = -9.89\hat i - 12.8 \hat j

now the direction of the velocity is given as

\theta = tan^{-1}(\frac{v_y}{v_x})

\theta = tan^{-1}(\frac{-12.8}{-9.89})

\theta = -127.7 degree

You might be interested in
Pulsed dye lasers emit light of wavelength 585 nm in 0.45 ms pulses to remove skin blemishes such as birthmarks. The beam is usu
koban [17]

Answer:

a) E₀ = 2.125 eV, b)     # photon2 = 9.2 10¹⁵ photons / mm²

Explanation:

a) To calculate the energy of a photon we use Planck's education

      E = h f

And the ratio of the speed of light

     c = λ f

We replace

      E = h c /λ

Let's calculate

      E₀ = 6.63 10⁻³⁴ 3 10⁸/585 10⁻⁹

      E₀ = 3.40 10⁻¹⁹ J

Let's reduce

     E₀ = 3.4 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

     E₀ = 2.125 eV

b) Let's look for the energy in each pulse

       P = E / t

       E = P t

       E = 20.0 0.45 10⁻³

       E = 9 10⁻³ J

let's use a ratio of proportions (rule of three) if we have the energy of a photon (E₀), to have the energy of 9 10⁻³ J

       # photon = 9 10⁻³ /3.40 10⁻¹⁹

      # photon = 2.65 10¹⁶ photons

Let's calculate the areas

Focus area

      A₁ = π r²

     A₁ = π (3.4/2)²

     A₁ = 9,079 mm²2

Area requested for calculation r = 1 mm

     A₂ = π 1²

     A₂ = 3.1459 mm²

 

Let's use another rule of three. If we have 2.65 106 photons in an area A1 how many photons in an area A2

    # photon2 = 2.65 10¹⁶ 3.1459 / 9.079

   # photon2 = 9.2 10¹⁵ photons / mm²

8 0
2 years ago
An opera singer who is a baritone, lowers his pitch and raises his voice for a song. Which best describes how the resulting soun
Usimov [2.4K]

Answer: 3.

Explanation:

The correct answer is a higher amplitude and lower frequency. Since an opera singer is lowering his pitch it means that he is creating higher amplitude and because he is raising his voice for a song with that higher amplitude he is creating lower frequency.

8 0
2 years ago
A 3.0 kg object is loaded into a toy spring gun, and the spring has a spring constant 750N/m. The object compresses the spring b
kiruha [24]

Answer:

Explanation:

mass of object, m = 3 kg

spring constant, K = 750 n/m

compression, x = 8 cm = 0.08 m

angle of gun, θ = 30°

(a) As the ball is launched, it has some velocity due to the compression in the spring, so it has some kinetic energy.

(b) Let v be th evelocity of ball at the tim eof launch.

by using the conservation of energy

1/2 Kx² = 1/2 mv²

750 x 0.08 x 0.08 = 3 x v²

v = 1.265 m/s

By use of the formula of maximum height

h = \frac{v^{2}Sin^{2}\theta}{2g}

h = \frac{1.265^{2}Sin^{2}30}{2\times 9.8}

h = 0.02 m

h = 2 cm  

4 0
3 years ago
These the flow of electrons (the current) and where some of the electrons' energy gets converted into heat. (Lessons 5.01-5.03)
liq [111]

Answer:

Conductors.

Explanation:

Conductors allow the flow of electrons i. e. the current and where some of the electrons energy gets converted into heat while some electrons energy converted into light. Conductors are the materials which has the ability to allow heat and electricity to flow through them. Metals such as gold, copper, Silver, Aluminum, Mercury, Steel, Iron and salty water etc are good conductors of heat and electricity.

3 0
2 years ago
How are Babys Born?​
My name is Ann [436]

Answer:

Baby are born due to the fertilization of Owen or egg present in vigina due to the fertilization from sperms

6 0
3 years ago
Read 2 more answers
Other questions:
  • Displacement vectors of 3 m and 5 m in the same direction combine to make a displacement vector that is _____ in magnitude.
    15·2 answers
  • 5. A car has a kinetic energy of 4.32x105 J when traveling at a speed of 23 m/s. What is
    14·1 answer
  • How many protons are in an atom of copper?
    7·2 answers
  • In which region of the electromagnetic spectrum is this radiation found?
    9·1 answer
  • Calculate the instantaneous speed of<br> an apple 8 seconds after being dropped<br> from rest.
    12·1 answer
  • Which type of light ray can produce identical but reversed
    10·2 answers
  • What would you need to do to find the number of neutrons in an atom?
    6·1 answer
  • What does it mean that a material transmits waves?
    15·1 answer
  • A car is moving with a velocity of45m/s. Is brought to rest in 5s.the distance travelled by car before it comes to rest is
    11·1 answer
  • DESPERATE!! WILL GIVE BARINLIST AND THANKS
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!