Answer:
the moment of inertia of the merry go round is 38.04 kg.m²
Explanation:
We are given;
Initial angular velocity; ω_1 = 37 rpm
Final angular velocity; ω_2 = 19 rpm
mass of child; m = 15.5 kg
distance from the centre; r = 1.55 m
Now, let the moment of inertia of the merry go round be I.
Using the principle of conservation of angular momentum, we have;
I_1 = I_2
Thus,
Iω_1 = I'ω_2
where I' is the moment of inertia of the merry go round and child which is given as I' = mr²
Thus,
I x 37 = ( I + mr²)19
37I = ( I + (15.5 x 1.55²))19
37I = 19I + 684.7125
37I - 19 I = 684.7125
18I = 684.7125
I = 684.7125/18
I = 38.04 kg.m²
Thus, the moment of inertia of the merry go round is 38.04 kg.m²
We can solve for the resultant x and y components by using
the sine and cosine functions.
resultant x = 2.5 cos 35 + 5.2 cos 22 = 6.87 km
resultant y = 2.5 sin 35 + 5.2 sin 22 = 3.38 km
The resultant displacement is calculated using hypotenuse
equation:
displacement = sqrt (6.87^2 + 3.38^2)
displacement = 7.66 km
The resultant angle is:
θ = tan^-1 (3.38 / 6.87)
θ = 26.20°
Therefore the magnitude and direction is:
7.66 km, 26.20° to the ground
<h3><u>Answer;</u></h3>
12.5 Newtons
<h3><u>Explanation;</u></h3>
Work done is defined as the product of force and distance covered or moved. It is measured in joules.
Work done = Force × distance
Therefore; making force the subject;
Force = work done/distance
= 50.0 J/ 4.00 m
=<u> 12.5 Newtons.</u>
For this problem, the working equation should be used from the Beer's Law:
A = ∈lc,
where
A is the absorbance
∈ is the molar absorptivity
l is the length of path of the cuvette diameter
C is the concentration of the sample placed inside the cuvette
Substituting the values:
0.417 = (4.50×10⁴ cm⁻¹ M⁻¹<span>)(1 cm)(C)
Solving for C:
C = 9.27</span>×10⁻⁶ M
