Answer:
(a) ω = 1.57 rad/s
(b) ac = 4.92 m/s²
(c) μs = 0.5
Explanation:
(a)
The angular speed of the merry go-round can be found as follows:
ω = 2πf
where,
ω = angular speed = ?
f = frequency = 0.25 rev/s
Therefore,
ω = (2π)(0.25 rev/s)
<u>ω = 1.57 rad/s
</u>
(b)
The centripetal acceleration can be found as:
ac = v²/R
but,
v = Rω
Therefore,
ac = (Rω)²/R
ac = Rω²
therefore,
ac = (2 m)(1.57 rad/s)²
<u>ac = 4.92 m/s²
</u>
(c)
In order to avoid slipping the centripetal force must not exceed the frictional force between shoes and floor:
Centripetal Force = Frictional Force
m*ac = μs*R = μs*W
m*ac = μs*mg
ac = μs*g
μs = ac/g
μs = (4.92 m/s²)/(9.8 m/s²)
<u>μs = 0.5</u>
Work done by a given force is given by

here on sled two forces will do work
1. Applied force by Max
2. Frictional force due to ground
Now by force diagram of sled we can see the angle of force and displacement
work done by Max = 

Now similarly work done by frictional force



Now total work done on sled


Answer:
The total volume of the air is 1000 cubic centimeters.
Explanation:
Since the bicycle pump and the bicycle tyre have the same pressure, then the total volume of the air is the sum of the volume of each element, then we translate this into the following artihmetical expression:


The total volume of the air is 1000 cubic centimeters.
Answer:
Y component = 32.37
Explanation:
Given:
Angle of projection of the rocket is, 
Initial velocity of the rocket is, 
A vector at an angle
with the horizontal can be resolved into mutually perpendicular components; one along the horizontal direction and the other along the vertical direction.
If a vector 'A' makes angle
with the horizontal, then the horizontal and vertical components are given as:

Here, as the velocity is a vector quantity and makes an angle of 33.6 with the horizontal, its Y component is given as:

Plug in the given values and solve for
. This gives,

Therefore, the Y component of initial velocity is 32.37.