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Luda [366]
3 years ago
15

While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find th

e motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 15 m, and you use your watch to find that each loop around takes 23 s.A. What is your speed?
B. What is the magnitude of your acceleration?
C. What is the ratio of your weight at the top of the ride to yourweight while standing on the ground?
D. What is the ratio of your weight at the bottom of the ride toyour weight while standing on the ground?
Physics
1 answer:
Dovator [93]3 years ago
6 0

Answer:

Explanation:

From the given information:

radius = 15 m

Time T = 23 s

a) Speed (v) = \dfrac{2 \pi r}{T}

v = \dfrac{2\times \pi \times 15}{23}

v = 4.10 m/s

b) The magnitude of the acceleration is:

a = \dfrac{v^2}{r} \\ \\ a = \dfrac{(4.10)^2}{15}

a = 1.12 m/s²

c) True weight = mg

Apparent weight = normal force

From the top;

the normal force = upward direction,

weight is downward as well as the acceleration.

true weight - normal force = ma  

apparent weight =mg - ma  

\dfrac{apparent \ weight}{true \  weight} = \dfrac{(mg - ma)}{(mg)}

=1- \dfrac{1.12}{9.8}

= 0.886 m/s²

d)

From the bottom;

acceleration is upward, so:

apparent weight - true weight = ma

apparent weight = true weight + ma

\dfrac{apparent \ weight }{true \ weight} =\dfrac{ mg + ma}{mg}

\dfrac{apparent \ weight }{true \ weight} =1+ \dfrac{a}{g} \\ \\ = 1 + \dfrac{1.12}{9.8}

= 1 + \dfrac{1.12}{9.8} \\ \\

= 1.114 m/s²

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Answer:

(a) the flow speed of the second section is 11 m/s

(b) the pressure of the second section is 6.33 x 10⁴ Pa

Explanation:

Given;

flow rate in the first section, Q₁ = 2750 cm³/sec

area of the first cross section, A₁ = 10 cm²

pressure in the first cross section, P₁ = 1.2 x 10⁵ Pa

area of the second section, A₂ = 2.5 cm²

(a) the flow speed of the second section (V₂)

Apply continuity equation;

Q₁ = Q₂

Q₁ = A₂V₂

V₂ = Q₁ / A₂

V₂ = (2750) / (2.5)

V₂ = 1100 cm/s = 11 m/s

(b) the pressure of the second section (P₂)

Apply Bernoulli's equation;

P₁ + ¹/₂ρV₁² = P₂ + ¹/₂ρV₂²

where;

ρ is density of water = 1000 kg/m³

V₁ is the speed of water in the first section;

Q₁ = A₁V₁

V₁ = Q₁ / A₁

V₁ = (2750) / (10)

V₁ = 275 cm/s = 2.75 m/s

P₂ = P₁ + ¹/₂ρV₁² - ¹/₂ρV₂²

P₂ = P₁ + ¹/₂ρ(V₁² - V₂²)

P₂ = 1.2 x 10⁵ Pa + ¹/₂ x 1000 (2.75² - 11²)

P₂ = 1.2 x 10⁵ Pa + 500(-113.438)

P₂ = 1.2 x 10⁵ Pa - 0.567  x 10⁵ Pa

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P₂ = 6.33 x 10⁴ Pa

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G a magnetic field perpendicular to the plane of a wire loop is uniform in space but changes with time t in the region of the lo
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Answer:

e = Δφ / Δt     induced emf is proportional to enclosed flux

Also φ  = B * A      flux is proportional to area and enclosed field

If the induced emf e increases with time than the flux and hence the magnetic field is increasing with time  (replace B with G)

Since e = ΔG * A / Δt    if e is linear then G must also be linear and be proportional to the time

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1 year ago
You are designing a simple elevator system for an old warehouse that is being converted to loft apartments. A 22,500-N elevator
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Answer:

A) mass = 3121.58 kg

B) tension = 25940.37 N

C) tension = 25940.37 N (tension on both sides will be the same)

Explanation:

Weight of elevator = 22500 N

Distance = 6.75 m

Time = 3 sec

Since it started from rest, initial speed is zero.

Using Newton's equation of motion we have,

S = ut + 0.5at^2

S = distance covered = 6.75 m

t = time = 3 s

a = acceleration upwards

u = initial velocity = 0

Substituting values, we have,

6.75 = 0(3) + (0.5 x a x 3^2)

6.75 = 4.5a

a = 6.75/4.5 = 1.5 m/s^2 (acceleration of the elevator upwards)

Mass of the elevator = Weight/g

Where g = acceleration due to gravity 9.81 m/s

Mass = 22500/9.81 = 2293.58 kg

From the image below we solve from

T - 22500 = ma

T - 22500 = 2293.58 x 1.5

T - 22500 = 3440.37

T = 3440.37 + 22500 = 25940.37 N (this is the tension on the rope)

On the other side,

mg - T = ma

9.81m - 25940.37 = 1.5m

(9.81 - 1.5)m = 25940.37

8.31m = 25940.37

m = 3121.58 kg (mass of counter weight)

See image below

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