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.
1 answer:
Refer to the figure shown below.
From the geometry,
y = 100 - (44 - 3) = 59 ft
From the Pythagorean theorem,
x² = 100² - 59² = 6519
x = 8007403 ft
Calculate the central angle, θ.
cos θ = 59/100 = 0.59
θ = 53.84° = 0.9397 radians
Calculate the arc length pq.
S = pq = 0.9394*100 = 93.94 ft
Calculate the angular velocity.
ω = (0.9397 radians)/(5 s) = 0.188 rad/s
Calculate the tangential velocity.
v = (100 ft)*(0.188 rad/s) = 18.8 ft/s
Calculate the time for 1 revolution.
T = (2π rad)/(0.188 rad/s) = 33.4 s
Answers:
The angular speed is 0.188 rad/s
The tangential speed is 18.8 ft/s
The time for one revolution is 33.4 s
From the geometry,
y = 100 - (44 - 3) = 59 ft
From the Pythagorean theorem,
x² = 100² - 59² = 6519
x = 8007403 ft
Calculate the central angle, θ.
cos θ = 59/100 = 0.59
θ = 53.84° = 0.9397 radians
Calculate the arc length pq.
S = pq = 0.9394*100 = 93.94 ft
Calculate the angular velocity.
ω = (0.9397 radians)/(5 s) = 0.188 rad/s
Calculate the tangential velocity.
v = (100 ft)*(0.188 rad/s) = 18.8 ft/s
Calculate the time for 1 revolution.
T = (2π rad)/(0.188 rad/s) = 33.4 s
Answers:
The angular speed is 0.188 rad/s
The tangential speed is 18.8 ft/s
The time for one revolution is 33.4 s
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Explanation:
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The unstretched length is
The initial speed is
The new length of the spring
The spring constant k is mathematically represented as
Where F is the force applied
y is the difference in weight which is
The negative sign is because the displacement of the spring (i.e its extension occurs against the force F)
Now substituting values accordingly
The elastic potential energy is given as
where D is this the is the displacement
Since Energy is conserved the total elastic potential energy would be
Substituting value accordingly
So to obtain total length we would add the unstretched length
So we have
Speed of the car given initially
v = 18 m/s
deceleration of the car after applying brakes will be
a = 3.35 m/s^2
Reaction time of the driver = 0.200 s
Now when he see the red light distance covered by the till he start pressing the brakes
Now after applying brakes the distance covered by the car before it stops is given by kinematics equation
here
vi = 18 m/s
vf = 0
a = - 3.35
so now we will have
So total distance after which car will stop is
So car will not stop before the intersection as it is at distance 20 m