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dedylja [7]
3 years ago
9

uppose a wheel is initially rotating at 10.0 rad/s while undergoing constant angular acceleration reaching a speed of 30.0 rad/s

after 36.0 seconds have elapsed. How long after the initial time has the wheel undergone half of the angular displacement that it will have gone through during the entire 36.0-second interval
Physics
1 answer:
Paul [167]3 years ago
8 0

Answer:

t = 22.2 s

Explanation:

angular distance covered in the 36.0 s is

θ = ω(avg)t = ½(10.0 + 30.0)36 = 720 radians

720/2 = 360 radians

α = Δω/t = (30 - 10)/36 = 5/9 rad/s²

θ = ω₀t + ½αt²

360 = 10.0t + ½(5/9)t²

   0 = (5/18)t² + 10.0t - 360

   0 = t² + 36t - 1296

t = (-36 ±√(36² - 4(1)(-1296))) / 2

t = (-36 ±√(6480)) / 2

t = -18 ±√1620

we ignore the negative time result as it occurs before we care.

t = -18 + √1620 = 22.249223... s

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3 years ago
A train has an acceleration of magnitude 0.90 m/s2 while stopping. A pendulum with a 0.55-kg bob is attached to a ceiling of one
anygoal [31]

The angle of the pendulum with the vertical is 5.2^{\circ}

Explanation:

As the train decelerates, the bob of the pendulum will feel a force given by

F=ma

where

m = 0.55 kg is the mass of the bob

a=0.9 m/s^2 is the magnitude of the acceleration

In the horizontal direction.

The pendulum will be inclined at an angle \theta from the vertical, so it will be in equilibrium, and therefore the horizontal component of the tension in the string must be equal to the net force F of the previous equation:

T sin \theta = ma (1)

where T is the tension in the string.

We also know that the bob is in equilibrium along the vertical direction: so the vertical component of the tension must be equal to the weight of the bob,

T cos \theta = mg (2)

where g=9.8 m/s^2 is the acceleration of gravity.

Dividing eq.(1) by eq(2), we get:

tan \theta = \frac{a}{g}

And therefore, we find the angle:

\theta=tan^{-1}(\frac{a}{g})=tan^{-1}(\frac{0.90}{9.8})=5.2^{\circ}

Learn more about forces and acceleration:

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3 0
3 years ago
theres two cups on a board - one half full and one empty. which one will fall off quicker while lifting the board up?
34kurt
The half empty will fall quicker

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2 years ago
If you push a crate with a force of 100 N and it slides at a constant speed and in the same direction, how much friction is acti
Nadusha1986 [10]

Answer: 100 N

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3 years ago
A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west and the total accelerati
lisov135 [29]

Answer with Explanation:

We are given that

Velocity,v=24 m/s west

Acceleration,a=2.5m/s^2

\theta=53^{\circ}(N of W)

Horizontal component of acceleration=Tangential acceleration

Tangential acceleration,a_x=acos\theta=2.5cos53=1.505 m/s^2

Radial acceleration=Vertical acceleration=a_y=asin\theta

a_y=2.5sin53=1.998 m/s^2

Radial acceleration,a_y=\frac{v^2}{R}

1.998=\frac{(24)^2}{R}

R=\frac{(24)^2}{1.998}

R=288.29 m

Time,t=\frac{2\pi R}{velocity}

t=\frac{2\pi(288.29)}{24}

t=75.47 s

8 0
3 years ago
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