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notsponge [240]
3 years ago
13

The driver of a car traveling at 23.1 m/s applies the brakes and undergoes a constant

Physics
1 answer:
Vsevolod [243]3 years ago
8 0

Answer:

The tires make 125 revolutions before the car stops

Explanation:

Circular and Linear Motion

A tire rotates around a fixed point and the tire when in contact with the ground, drives a vehicle in a linear path. This is an example of a relationship between both types of movements that can be taking place simultaneously.

The car is moving with an initial speed of v_o=23.1\ m/s and then breaks at a=-1.03\ m/s^2 until it stops. We can compute the time take to stop by using

\displaystyle v_f=v_o+a.t

Solving for t

\displaystyle t=\frac{v_f-v_o}{a}

Putting in numbers

\displaystyle t=\frac{0-23.1}{-1.03}

\displaystyle t=22.427\ sec

Now, let's transfer this information to the circular motion. We know the tangent speed is

\displaystyle v_t=w.r

Being w the angular speed and r the radius of the circle, in this case, the tires. The tangent speed is the same as the speed of motion of the car. It gives us the initial angular speed

\displaystyle w_o=\frac{v_t}{r}

\displaystyle w_o=\frac{23.1}{0.33}=70\ rad/s

When the circular motion is not uniform, i.e. there is angular acceleration \alpha, the angular speed is a function of time

\displaystyle w=w_o+\alpha t

We can compute the angular acceleration knowing the final angular speed is zero when the car stops.

\displaystyle \alpha=\frac{w-w_o}{t}=\frac{0-70}{22.427}

\displaystyle \alpha=-3.121\ rad/s^2

The rotation angle is also a function of time as shown

\displaystyle \theta=w_o\ t+\frac{\alpha t^2}{2}

Using the given and computed values

\displaystyle =70(22.427)-\frac{3.121(22.427)^2}{2}

\displaystyle \theta =784.95\ rad

Knowing each revolution is 2\pi radians, the number of revolutions is

\displaystyle n=\frac{\theta }{2\pi}=125\ rev

The tires make 125 revolutions before the car stops

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A spherical gas-storage tank with an inside diameter of 9 m is being constructed to store gas under an internal pressure of 1.50
lutik1710 [3]

Answer: 33 mm

Explanation:

Given

Diameter of the tank, d = 9 m, so that, radius = d/2 = 9/2 = 4.5 m

Internal pressure of gas, P(i) = 1.5 MPa

Yield strength of steel, P(y) = 340 MPa

Factor of safety = 0.3

Allowable stress = 340 * 0.3 = 102 MPa

σ = pr / 2t, where

σ = allowable stress

p = internal pressure

r = radius of the tank

t = minimum wall thickness

t = pr / 2σ

t = 1.5*10^6 * 4.5 / 2 * 102*10^6

t = 0.033 m

t = 33 mm

The minimum thickness of the wall required is therefore, 33 mm

6 0
3 years ago
A thermistor is placed in a 100 °C environment and its resistance measured as 20,000 Ω. The material constant, β, for this therm
Karo-lina-s [1.5K]

Answer:

the thermistor temperature = 325.68 \ ^0 \ C

Explanation:

Given that:

A thermistor is placed in a 100 °C environment and its resistance measured as 20,000 Ω.

i.e Temperature

T_1 = 100^0C\\T_1 = (100+273)K\\\\T_1 = 373\ K

Resistance of the thermistor R_1 = 20,000 ohms

Material constant \beta = 3650

Resistance of the thermistor R_2 = 500 ohms

Using the equation :

R_1 = R_2  \ e^{\beta} (\frac{1}{T_1}- \frac{1}{T_2})

\frac{R_1}{ R_2} =   \ e^{\beta} (\frac{1}{T_1}- \frac{1}{T_2})

Taking log of both sides

In \ \frac{R_1}{ R_2} = In \  \ e^{\beta} (\frac{1}{T_1}- \frac{1}{T_2})

In \ \frac{R_1}{ R_2} = {\beta} (\frac{1}{T_1}- \frac{1}{T_2})

\frac{ In \ \frac{R_1}{ R_2}}{ {\beta}} = (\frac{1}{T_1}- \frac{1}{T_2})

\frac{1}{T_2} =   \frac{1}{T_1}  -          \frac{ In \ \frac{R_1}{ R_2}}{ {\beta}}

{T_2} =  \frac{\beta T_1}{\beta - In (\frac{R_1}{R_2})T}

Replacing our values into the above equation :

{T_2} =  \frac{3650*373}{3650 - In (\frac{20000}{500})373}

{T_2} =  \frac{1361450}{3650 - 3.6888*373}

{T_2} =  \frac{1361450}{3650 - 1375.92}

{T_2} =  \frac{1361450}{2274.08}

{T_2} = 598.68 \ K

{T_2} = 325.68 \ ^0 \ C

Thus, the thermistor temperature = 325.68 \ ^0 \ C

4 0
3 years ago
A shoe and a shirt are released from the same height. They take different amounts of time to fall to the ground. How can this be
Law Incorporation [45]

The best explanation for the difference in time is: A. The difference in weight doesn't affect the time, but they are affected differently by air resistance.

<h3>What is weight?</h3>

Weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Also, the weight of an object (body) is typically measured in Newton.

<h3>The factors that affect weight.</h3>

Some of the factors that affect the weight that is possessed by an object or a physical body include the following:

  • Mass
  • Distance
  • Air resistance

In conclusion, the weight possessed by the shoe and shirt has no effect on time but would be affected differently by air resistance.

Read more on weight here: brainly.com/question/13833323

4 0
2 years ago
True or False: Objects that have more mass also have more gravity.
Fantom [35]

Answer:

True

Explanation:

The smaller object usually moves towards the larger object, because the larger object has more mass than the smaller object, so it has a larger gravitational pull.

7 0
3 years ago
Read 2 more answers
Two small metal spheres are 25 cm apaft.The spheres have equal amount of negative charge and repel each other with a force of 0.
Mars2501 [29]

Answer:

0.5\times 10^{-6}C

Explanation:

According to coulombs law force between two charges is given by F=\frac{1}{4\pi \epsilon _0}\frac{Q_1Q_2}{R^2} here R is the distance between both the charges which is given as 25 cm

We have given force F =0.036 N

So  0.036=\frac{1}{4\pi \times 8.85\times 10^{-12}}\frac{Q^2}{(0.25^2)} As \epsilon _0 is constant which value is 8.85\times 10^{-12}

Q^2=0.250\times 10^{-12}

Q=0.5\times 10^{-6}C

8 0
3 years ago
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