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Lelechka [254]
3 years ago
14

A 110-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 0.600 rev/s in 2.00 s
Physics
1 answer:
sweet [91]3 years ago
8 0

Answer:

155 N

Explanation:

We are given following data for a uniform, solid, horizontal disk:  

r = 1.5 m

m= 110 kg

t=2 s

w = 0.6  

Torque is given by:  

т = F*r

  =I*α

Solving it for the force exerted on the rope:  

F = I*α/r

  = (1/2*m*r^2)*(2π*w/t )/r

  = (1/2*110*1.5^2)*(2π*0.6/2 )/1.5

  = 155 N

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A car accelerates uniformly from rest and
miv72 [106K]

Answer:

29.75 revolutions

Explanation:

The kinematic formula for distance, given a uniform acceleration a and an initial velocity v₀, is

d=v_0t+\frac{1}{2}at^2

This car is starting from rest, so v₀ = 0 m/s. Additionally, we have a = 9.2/9.7 m/s² and t = 9.7 s. Plugging these values into our equation:

d=0t+\frac{1}{2}\left(\frac{9.2}{9.7}\right)(9.7)^2\\d=\frac{1}{2}(9.2)(9.7)\\d=4.6(9.7)\\d=44.62

So, the car has travelled 44.62 m in 9.7 seconds - we want to know how many of the tire's <em>circumferences</em> fit into that distance, so we'll first have to calculate that circumference. The formula for the circumference of a circle given its diameter is c=\pi{d}, which in this case is 47.8π cm, or, using π ≈ 3.14, 47.8(3.14) = 150.092 cm.

Before we divide the distance travelled by the circumference, we need to make sure we're using the same units. 1 m = 100 cm, so 105.092 cm ≈ 1.5 m. Dividing 44.62 m by this value, we find the number of revs is

44.62/1.5\approx29.75 revolutions

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Shakina and Juliette set the car's initial velocity to zero and set the acceleration to +1.2 m/s2, then clicked "start." Answer
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Let's start by differentiating the terms distance and displacement. They both refer to the length of paths. Distance only accounts for the total length regardless of the path taken. Displacement measures the linear path from the starting point to the end point. So, it does not necessarily follow the actual path. However, for this problem, assuming that the path is just in one direction, displacement and distance would just be equal. The equation would be:

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