What is the angular width of a person's thumb viewed at arm's length? Assume that the width of the thumb is 17.3 mm and that the distance between the eyes and the thumb is 71.9 cm. Use the small-angle approximation and then convert the answer to degrees.

Answers

Answer 1

Answer:

Answer:

$\theta_(degrees) =0.024\°=0\°1'26.62''$

Explanation:

To solve the problem it is necessary to take into account the concepts related to arc length and the radius that make up the measurements of an angle.

An angle is given by the length of arc displaced as a function of the radius, that is

$\theta = (Arc_(length))/(Radius)$

$\theta = (17.3*10^(-3))/(71.9*10^(-2))$

$\theta = 0.02406rad$

360° is equal to do $2\pi$ rad, therefore:

$\theta_(degrees) = 0.02406rad *((180\°)/(2\pi rad))$

$\theta_(degrees) =0.024\°=0\°1'26.62''$

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Draw a ray diagram for an object placed more than two focal lengths in front of a converging lens.

Answers

Answer:

Explanation:

There is a convex lens M N is placed. An object AB is placed at a distance more than two focal lengths of the lens.

A ray of light is starting from point A and parallel to the principal axis, then after refraction it goes from the focus.

Another ray which goes through the optical centre of the lens becomes undeviated after refraction.

The two refracted rays meet at the point A', So A'B is the image of AB.

The nature of image is real, inverted and diminished.

An earthquake 45 km from a city produces P and S waves that travel outward at 5000 m/s and 3000 m/s, respectively. Once city residents feel the shaking of the P wave, how much time do they have before the S wave arrives in seconds?

Answers

Answer:

The S wave arrives 6 sec after the P wave.

Explanation:

Given that,

Distance of P = 45 km

Speed of p = 5000 m/s

Speed of S = 3000 m/s

We need to calculate the time by the P wave

Using formula of time

$t = (D)/(v)$

Where, D = distance

v = speed

t = time

Put the value in to the formula

$t_(p) =(45*1000)/(5000)$

$t_(p) = 9\ sec$

Now, time for s wave

$t_(s)=(45000)/(3000)$

$t =15\ sec$

The required time is

$\Delta t=t_(s)-t_(p)$

$\Delta t=15-9$

$\Delta t =6\ sec$

Hence, The S wave arrives 6 sec after the P wave.

Assume: The bullet penetrates into the block and stops due to its friction with the block.

The compound system of the block plus the

bullet rises to a height of 0.13 m along a

circular arc with a 0.23 m radius.

Assume: The entire track is frictionless.

A bullet with a m1 = 30 g mass is fired

horizontally into a block of wood with m2 =

4.2 kg mass.

The acceleration of gravity is 9.8 m/s2 .

Calculate the total energy of the composite

system at any time after the collision.

Answer in units of J.

Taking the same parameter values as those in

Part 1, determine the initial velocity of the

bullet.

Answer in units of m/s.

Answers

To solve this problem we will start considering the total energy of the system, which is given by gravitational potential energy of the total of the masses. So after the collision the system will have an energy equivalent to,

$E_T = (m_1+m_2)gh$

Here,

$m_1$ = mass of bullet

$m_2$ = Mass of Block of wood

The ascended height is 0.13m, so then we will have to

PART A)

$E_T = (m_1+m_2)gh$

$E_T = (0.03+4.2)(9.8)(0.13)$

$E_T = 5.389J$

PART B) At the same time the speed can be calculated through the concept provided by the conservation of momentum.

$m_1v_1+m_2v_2 = (m_1+m_2)v_f$

Since the mass at the end of the impact becomes only one in the system, and the mass of the block has no initial velocity, the equation can be written as

$m_1v_1 =(m_1+m_2)v_f$

The final velocity can be calculated through the expression of kinetic energy, so

$E_T = KE = (1)/(2) (m_1+m_2)v_f^2$

$v_f = \sqrt{(2E_T)/(m_1+m_2)}$

$v_f = \sqrt{(2*5.389J)/(0.03+4.2)}$

$v_f = 1.5962m/s$

Using this value at the first equation we have that,

$m_1v_1 = (m_1+m_2)v_f$

$v_1 =((m_1+m_2)v_f)/(m_1)$

$v_1 = ((0.03+4.2)(1.5962))/(0.03)$

$v_1 = 225.06m/s$

A model airplane with a mass of 0.741kg is tethered by a wire so that it flies in a circle 30.9 m in radius. The airplane engine provides anet thrust of 0.795 N perpendicular tothe tethering wire.(a) Find the torque the net thrust producesabout the center of the circle.
N·m

(b) Find the angular acceleration of the airplane when it is inlevel flight.
rad/s2

(c) Find the linear acceleration of the airplane tangent to itsflight path.
m/s2

Answers

(a) 24.6 Nm

The torque produced by the net thrust about the center of the circle is given by:

$\tau = F r$

where

F is the magnitude of the thrust

r is the radius of the wire

Here we have

F = 0.795 N

r = 30.9 m

Therefore, the torque produced is

$\tau = (0.795 N)(30.9 m)=24.6 N m$

(b) $0.035 rad/s^2$

The equivalent of Newton's second law for a rotational motion is

$\tau = I \alpha$

where

$\tau$ is the torque

I is the moment of inertia

$\alpha$ is the angular acceleration

If we consider the airplane as a point mass with mass m = 0.741 kg, then its moment of inertia is

$I=mr^2 = (0.741 kg)(30.9 m)^2=707.5 kg m^2$

And so we can solve the previous equation to find the angular acceleration:

$\alpha = (\tau)/(I)=(24.6 Nm)/(707.5 kg m^2)=0.035 rad/s^2$

(c) $1.08 m/s^2$

The linear acceleration (tangential acceleration) in a rotational motion is given by

$a=\alpha r$

where in this problem we have

$\alpha = 0.035 rad/s^2$ is the angular acceleration

r = 30.9 m is the radius

Substituting the values, we find

$a=(0.035 rad/s^2)(30.9 m)=1.08 m/s^2$

Nichrome wire, often used for heating elements, has resistivity of 1.0 × 10-6 Ω ∙ m at room temperature. What length of No. 30 wire (of diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature?

Answers

Answer:

Length = 2.453 m

Explanation:

Given:

Resistivity of the wire (ρ) = 1 × 10⁻⁶ Ω-m

Diameter of the wire (d) = 0.250 mm = 0.250 × 10⁻³ m

Resistance of the wire (R) = 50 Ω

Length of the wire (L) = ?

The area of cross section is given as:

$A=(1)/(4)\pi d^2\n\nA=(1)/(4)*\ 3.14* (0.250* 10^(-3))^2\n\nA=0.785* 6.25* 10^(-8)\n\nA=4.906* 10^(-8)\ m^2$

We know that, for a constant temperature, the resistance of a wire is directly proportional to its length and inversely proportional to its area of cross section. The constant of proportionality is called the resistivity of the wire. Therefore,

$R=\rho (L)/(A)$

Expressing the above in terms of length 'L', we get:

$L=(RA)/(\rho)$

Plug in the given values and solve for 'L'. This gives,

$L=(50* 4.906* 10^(-8))/(1* 10^(-6))\ m\n\nL=(2.453)/(1)=2.453\ m$

Therefore, length of No. 30 wire (of diameter 0.250 mm) is 2.453 m.

Crude oil is a mixture of many different components. The extraction of crude oil from the Earth is important, but its refinement into different substances is a key piece to obtaining as many uses as possible from the crude oil. Using the diagram, justify the source of data used to develop the technology for refining the crude oil.

Answers

Crude oil is a mixture of nitrogen, oxygen, sulphur, and hydrogen components

What is Crude oil?

A combination of hydrocarbons known as crude oil is one that is found in naturally occurring subsurface reservoirs in the liquid phase and continues to be liquid at atmospheric pressure after passing through surface separation equipment.

Refineries transform crude oil into useful products including gasoline, diesel, and aviation fuels for transportation. Gasoline: A fuel used in both personal and commercial vehicles that are made for internal combustion engines.

In addition to some nitrogen, sulphur, and oxygen, crude oil is a combination of very flammable liquid hydrocarbons (compounds mostly made of hydrogen and carbon).

More about the Crude oil link is given below.

brainly.com/question/351648

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Answer: Different fuel components boil at different temperatures, allowing them to be separated.

Explanation:

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