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scoray [572]
3 years ago
10

The position vector of a particle of mass 1.65 kg as a function of time is given by = (6.00 î + 4.15 t ĵ), where is in meters an

d t is in seconds. Determine the angular momentum of the particle about the origin as a function of time.
Physics
1 answer:
SashulF [63]3 years ago
7 0

Answer:

 L = 41.09 Kg m2 / s      The angular momentum does not depend on the time

Explanation:

The definition of angular momentum is

        L = r x p

Where blacks indicate vectors

Let's apply this definition our case. Linear momentum

      p = m v

Let's replace

      L = m r x v

The given function is

      x = 6.00 i ^ + 4.15 t j ^

We look for speed

     v = dx / dt

     v = 0 + 4.15 j ^

To evaluate the angular momentum one of the best ways is to use determinants

     L = m \left[\begin{array}{ccc}i&j&k\\6&4.15t&0\\0&4.15&0\end{array}\right]

      L = m 6 4.15 k ^

The other products give zero

Let's calculate

      L = 1.65 6 4.15 k ^

      L = 41.09 Kg m2 / s

The angular momentum does not depend on the time

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When an electron moves 2.5 m in the direction of an electric field, the change in electrical potential energy of the electron is
anygoal [31]
In the field of electromagnetism, when two charged plates that are situated opposite to each other by a certain distance, it forms an energy called the electric field. This energy is due to the difference in potential energy with respect to distance. Thus,

E = V/d

However, the voltage in volts is energy per coulomb. Thus,
V = (8x10-17 J/electron)*(1electron/1.60218x10^-19 C)
V = 499.32 volts

Therefore,

E = 499.32 volts /2.5 m
E = 199.73 N/C

The electric field that caused the change in potential energy is equal to 199.73 Newtons per Coulomb.
7 0
3 years ago
Light of wavelength 560 nm passes through a slit of width 0. 170 mm. (a) the width of the central maximum on a screen is 8. 00 m
faltersainse [42]

The distance between slit and the screen is 1.214m.

To find the answer, we have to know about the width of the central maximum.

<h3>How to find the distance between slit and the screen?</h3>
  • It is given that, wavelength 560 nm passes through a slit of width 0. 170 mm, and the width of the central maximum on a screen is 8. 00 mm.
  • We have the expression for slit width w as,

                           w=\frac{2*wavelength*d}{a}

where, d is the distance between slit and the screen, and a is the slit width.

  • Thus, distance between slit and the screen is,

                           d=\frac{w*a}{2*wavelength} =\frac{8*10^{-3}*0.17*10^{-3}}{560*10^{-9}*2} \\\\d=1.214m

Thus, we can conclude that, the distance between slit and the screen is 1.214m.

Learn more about the width of the central maximum here:

brainly.com/question/13088191

#SPJ4

3 0
2 years ago
Fiber optics are an important part of our modern internet. In these fibers, two different glasses are used to confine the light
motikmotik

Answer:

n_cladding = 1.4764

Explanation:

We are told that θ_max = 5 °

Thus;

θ_max + θ_c = 90°

θ_c = 90° - θ_max

θ_c = 90° - 5°

θ_c = 85°

Now, critical angle is given by;

θ_c = sin^(-1) (n_cladding/n_core)

sin θ_c = (n_cladding/n_core)

n_cladding = (n_core) × sin θ_c

Plugging in the relevant values, we have;

n_cladding = 1.482 × sin 85

n_cladding = 1.4764

7 0
3 years ago
You drop a pencil from your desk, which is 1 meter above the floor. How long does it take for the pencil to hit the floor? How f
vova2212 [387]

Answer:

1. 0.45 s.

2. 4.41 m/s

Explanation:

From the question given above, the following data were obtained:

Height (h) = 1 m

Time (t) =?

Velocity (v) =?

1. Determination of the time taken for the pencil to hit the floor.

Height (h) = 1 m

Acceleration due to gravity (g) = 9.8 m/s²

Time (t) =?

h = ½gt²

1 = ½ × 9.8 × t²

1 = 4.9 × t²

Divide both side by 4.8

t² = 1/4.9

Take the square root of both side

t = √(1/4.9)

t = 0.45 s.

Thus, it will take 0.45 s for the pencil to hit the floor.

2. Determination of the velocity with which the pencil hit the floor.

Initial velocity (u) = 0 m/s

Acceleration due to gravity (g) = 9.8 m/s²

Time (t) = 0.45 s.

Final velocity (v) =?

v = u + gt

v = 0 + (9.8 × 0.45)

v = 0 + 4.41

v = 4.41 m/s

Thus, the pencil hit the floor with a velocity of 4.41 m/s

6 0
3 years ago
In a closed system, a cart with a mass of 1.5 kg is rolling to the right at 1.4 m/s, while another cart of mass 1.0 kg is rollin
bija089 [108]

Answer: The correct option is (c.).

Explanation:

Mass of the cart A= 1.5 kg

Velocity of Cart A = 1.4 m/s towards right

Mass of the cart B = 1.0 kg

Velocity of Cart B = 1.4 m/s towards left

Momentum (P)= Mass × Velocity

P_A=1.5 kg\times 1.4 m/s=2.1 kg m/s

P_B=1.0 kg\times (-1.4m/s)=-1.4 kg m/s

(Negative sign means velocity of the cart is in opposite direction of that of the cart A)

Total Momentum =P_A+P_B=2.10 kg m/s-1.40 kg m/s=0.70 kg m/s

Hence, the correct option is (c.).

7 0
3 years ago
Read 2 more answers
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