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kotykmax [81]
3 years ago
6

A 125-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope a

bout the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.700 rev/s in 2.00 s? (State the magnitude of the force.)
Physics
1 answer:
lbvjy [14]3 years ago
4 0

Answer:

201.6 N

Explanation:

m = mass of disk shaped merry-go-round = 125 kg

r = radius of the disk = 1.50 m

w₀ = Initial angular speed = 0 rad/s

w = final angular speed = 0.700 rev/s = (0.700) (2π) rad/s = 4.296 rad/s

t = time interval = 2 s

α = Angular acceleration

Using the equation

w = w₀ + α t

4.296 = 0 + 2α

α = 2.15 rad/s²

I = moment of inertia of merry-go-round

Moment of inertia of merry-go-round is given as  

I = (0.5) m r² = (0.5) (125) (1.50)² = 140.625 kgm²

F = constant force applied

Torque equation for the merry-go-round is given as

r F = I α

(1.50) F = (140.625) (2.15)

F = 201.6 N

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Answer:

a = 2 m/s^2

which agrees with the third answer option provided.

Explanation:

Recall the kinematic formula for displacement under the action of a constant acceleration "a":

yf - yi = 1/2 a  t^2

using the information provided this equation becomes:

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solve for a:

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3 years ago
If you have 10.0 g of a substance that decays with a half-life of 14 days, then how much will you have after 42 days?
Nat2105 [25]
The formula for the mass that remains:
m=m_0 \times (\frac{1}{2})^\frac{t}{T}
m₀ - the initial mass, t - time, T - the half-life

m_0=10 \ g \\
T=14 \ d \\
t=42 \ d \\ \\
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The distance between the two Big Ben and the Empire State Building, r = 5,000,000 meters

By Newton's Law of gravitation, we have;

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