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rodikova
3 months ago
7

A ferris wheel of radius 100 feet is rotating at a constant angular speed Ï rad/sec counterclockwise. using a stopwatch, the rid

er finds it takes 5 seconds to go from the lowest point on the ride to a point q, which is level with the top of a 44 ft pole. assume the lowest point of the ride is 3 feet above ground level.

Physics
1 answer:
Ostrovityanka [3.2K]3 months ago
4 0
Refer to the image below.

From the geometry, the height is calculated as follows: y = 100 - (44 - 3) = 59 ft.
Using the Pythagorean theorem,
x² = 100² - 59² = 6519
Thus, x = 80.07403 ft.

Now to find the central angle, θ,
cos θ = 59/100 = 0.59
Therefore, θ is approximately 53.84° or 0.9397 radians.

Next, we will calculate the arc length pq.
Arc length S = pq = 0.9394*100 = 93.94 ft.

Now, for angular velocity,
ω = (0.9397 radians)/(5 s) = 0.188 rad/s.

Let’s calculate tangential velocity.
v = (100 ft)*(0.188 rad/s) = 18.8 ft/s.

Finally, determine the time for one complete revolution.
T = (2π rad)/(0.188 rad/s) = 33.4 s.

Summary of results:
The angular velocity is 0.188 rad/s.
The tangential velocity measures 18.8 ft/s.
The duration for a single revolution is 33.4 seconds.

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Answer:

b) TA = TB = TC

Explanation:

  • When the blocks are brought into contact and isolated from the environment, they will exchange heat until they achieve thermal equilibrium.
  • During this exchange, the hotter body will lose heat, which will be gained by the cooler body.
  • The equilibrium state will be established once this equation is satisfied:

       \Delta Q = c_{st}* m_{A} * (T_{fin} - T_{0A} ) = c_{st}* m_{B} * (T_{0B} - T_{fin} )

  • Substituting the initial temperatures T₀A = 300º C and T₀B = 400ºC, while simplifying for equal block masses mA = mB, enables us to solve for the final temperature, Tfin:

       (400 \ºC - T_{fin}) = (T_{fin} - 300 \ºC) \\ \\ 2* T_{fin} = 700\ºC\\ \\ T_{fin} = 350\ºC

  • At equilibrium, when both blocks combine, they will yield a uniform final temperature of 350ºC.
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3 months ago
A spring with a spring constant of 0.70 N/m is stretched 1.5 m. What was the force?
inna [3103]

Answer:

1.05 N

Explanation:

K = 0.7 N/m

e = 1.5 m

F =?

According to Hooke's law:

F = Ke

= 0.7×1.5

= 1.05 N

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Find the three longest wavelengths (call them λ1, λ2, and λ3) that "fit" on the string, that is, those that satisfy the boundary
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For a string that is secured at both ends, the oscillation amplitude must be zero at both extremities of the string. Refer to the attached images for clarity. It is evident that our fundamental harmonic will have the following wavelength: All subsequent harmonics are simply multiples of the fundamental. The three longest wavelengths are as follows:
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A team of engineering students is testing their newly designed 200 kg raft in the pool where the diving team practices. The raft
Sav [3153]

Answer:

The water level increases more when the cube is above the raft before it sinks.

Explanation:

The principle involved is based on Archimedes' theory, which states that immersing an object in water will raise the initial water level. This means that the height of the water in the container increases. The increase in water volume corresponds to the volume of the submerged object.

We can consider two scenarios: when the steel cube rests on the raft and when it settles at the pool's bottom.

When the cube rests at the pool’s bottom, the volume will indeed rise, and we can ascertain this using the cube's volume.

Vc = 0.45*0.45*0.45 = 0.0911 [m^3]

When an object floats, it's because the densities of the object and water are in equilibrium.

Ro_{H2O}=R_{c+r}\\where:\\Ro_{H2O}= water density = 1000 [kg/m^3]\\Ro_{c+r}= combined density cube + raft [kg/m^3]

The formula for density is:

Ro = m/V

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m= mass [kg]

V = volume [m^3]

The buoyant force can be calculated with this equation:

F_{B}=W=Ro_{H20}*g*Vs\\W = (200+730)*9.81\\W=9123.3[N]\\\\9123=1000*9.81*Vs\\Vs = 0.93 [m^3]

Vs > Vc indicates that the combined volume of the raft and the cube exceeds that of the cube alone resting at the bottom of the pool. Hence, when the cube is positioned above the raft, the water level rises more before it becomes submerged.

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