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Lera25 [3.4K]
2 years ago
10

You go to an amusement park with your friend Betty, who wants to ride the 80-m-diameter Ferris wheel. She starts the ride at the

lowest point of a wheel that, as you face it, rotates counterclockwise.
Part A

What is the magnitude of her displacement vector when the wheel has rotated by an angle of 40 ∘?

Express your answer with the appropriate units.

Part B

What is the direction of her displacement vector when the wheel has rotated by an angle of 40 ∘, measured counterclockwise from the horizontal?
Physics
1 answer:
elena-s [515]2 years ago
8 0

Answer:

A. 27.4 m

B. 0.35 rad or 20 degrees

Explanation:

A Ferris wheel with 80m in diameter would have a radius of 40m

Let the center of the wheel be the origin, so the vector (let call it a) from the the center of the wheel to Betty's starting (lowest) point is

\vec{a} =

When the wheel rotated by 40 degrees, Betty would have traveled a distance of:

horizontally rsin\theta = 40sin40^0 = 25.71 m

vertically r - rcos\theta = 40 - 40cos40^0 = 9.36 m

So her displacement vector is <25.71, 9.36>

A. Magnitude of this vector is

\sqrt{25.71^2 + 9.36^2} = 27.4 m

B. Direction of this vector is

tan\alpha = 9.36 / 25.71 = 0.364

\alpha = tan^{-1}0.364 = 0.35 rad or 20 degrees

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A closed, rigid container holding 0.2 moles of a monatomic ideal gas is placed over a Bunsen burner and heated slowly, starting
Georgia [21]

Answer:

a) 2250 J

b) 0 J

c) 2250 J

Explanation:

a) Since, the process is isochoric

the change in internal energy

\Delta U = n C_v(T_f-T_i)

Here, n = 0.2 moles

Cv = 12.5 J/mole.K

We have to find T_f so we can use gas equation as

\frac{P_1V_1}{P_2V_2} =\frac{T_i}{T_f}\\Since, V_1=V_2    [isochoric/process]\\\Rightarrow \frac{P_{atm}}{4P_{atm}} = \frac{300}{T_f} \\\Rightarrow T_f = 1200 K

So,  \Delta U= 0.2\times12.5(1200-300)\\=2250 J

b) Since, the process is isochoric no work shall be done.

c) By first law of thermodynamics we have

\Delta U = Q-W\\Since, W = 0\\\Delta U = Q\\Therefore, Q = 2250 J

Since, Q is positive 2250 J of heat will flow into the system.

6 0
1 year ago
A two-resistor voltage divider employing a 2-k? and a 3-k? resistor is connected to a 5-V ground-referenced power supply to prov
vesna_86 [32]

Answer:

circuit sketched in first attached image.

Second attached image is for calculating the equivalent output resistance

Explanation:

For calculating the output voltage with regarding the first image.

Vout = Vin \frac{R_{2}}{R_{2}+R_{1}}

Vout = 5 \frac{2000}{5000}[/[tex][tex]Vout = 5 \frac{2000}{5000}\\Vout = 5 \frac{2}{5} = 2 V

For the calculus of the equivalent output resistance we apply thevenin, the voltage source is short and current sources are open circuit, resulting in the second image.

so.

R_{out} = R_{2} || R_{1}\\R_{out} = 2000||3000 = \frac{2000*3000}{2000+3000} = 1200

Taking into account the %5 tolerance, with the minimal bound for Voltage and resistance.  

if the -5% is applied to both resistors the Voltage is still 5V because the quotient  has 5% / 5% so it cancels. to be more logic it applies the 5% just to one resistor, the resistor in this case we choose 2k but the essential is to show that the resistors usually don't have the same value. applying to the 2k resistor we have:

Vout = 5 \frac{1900}{4900}\\Vout = 5 \frac{19}{49} = 1.93 V

Vout = 5 \frac{2100}{5100}\\Vout = 5 \frac{21}{51} = 2.05 V

R_{out} = R_{2} || R_{1}\\R_{out} = 1900||2850= \frac{1900*2850}{1900+2850} = 1140

R_{out} = R_{2} || R_{1}\\R_{out} = 2100||3150 = \frac{2100*3150 }{2100+3150 } = 1260

so.

V_{out} = {1.93,2.05}V\\R_{1} = {1900,2100}\\R_{2} = {2850,3150}\\R_{out} = {1140,1260}

4 0
2 years ago
A car is traveling at 20 meters/second and is brought to rest by applying brakes over a period of 4 seconds. What is its average
frez [133]
 (u) = 20 m/s 
(v) = 0 m/s 
<span> (t) = 4 s 
</span>
<span>0 = 20 + a(4) 

</span><span>4 x a = -20 
</span>
so, the answer is <span>-5 m/s^2. or -5 meter per second</span>
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W=ΔKE , W=-5000j
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4 0
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