Respuesta :
Given Information:
kinetic energy = E = 0.15 J
mass = m = 100g = 0.1 kg
diameter = d = 8.0 cm = 0.08 m
Required Information:
Speed = v = ?
Answer:
v = 2.44 m/s
Explanation:
First convert diameter into radius
r = d/2 = 0.08/2 = 0.04 m
The moment of inertia of disc is given by
I = 0.5mr²
Where m is the mass and r is the radius of the disk
I = 0.5(0.1)(0.04)²
I = 0.00008 kg.m²
and since we are dealing with rotational motion then rotational kinetic energy is given by
E = 0.5 I ω²
we have to separate ω
ω² = E/0.5 I
ω = √E/0.5 I
ω = √0.15/0.5(0.00008)
ω = 61.23 rad/sec
Finally we know that speed is given as
v = ω r
v = 61.23 (0.04)
v = 2.44 m/s
Therefore, the speed of a point on the rim is 2.44 m/s
The speed of a point on the rim is equal to 2.45 meters per seconds.
Given the following data:
- Mass of disk = 100 g
- Diameter of disk = 8 cm
- Kinetic energy = 0.15 Joules
Conversion:
Diameter of disk = 8 cm to m = [tex]\frac{8}{100}[/tex] = 0.08 meters
Mass of disk = 100 g to kg = [tex]\frac{100}{1000}[/tex] = 0.1 kg
Radius = [tex]\frac{diameter}{2} = \frac{0.08}{2}[/tex] = 0.04 m
To find the speed of a point on the rim:
First of all, we would determine the moment of inertia (I) of the disk.
[tex]I = \frac{1}{2} mr^2\\\\I = \frac{1}{2} \times 0.1 \times 0.04^2\\\\I = 0.05 \times 0.0016[/tex]
Moment of inertia, I = 0.00008 [tex]kgm^2[/tex]
Next, we would solve for angular velocity from the rotational kinetic energy of the disk:
[tex]E_R = \frac{1}{2} Iw^2\\\\0.15 = \frac{1}{2} \times 0.00008 \times w^2\\\\0.3 = 0.00008w^2\\\\w^2 = \frac{0.3}{0.00008} \\\\w^2 = 3750\\\\w = \sqrt{3750}[/tex]
Angular velocity, w = 61.24 rad/s
Now, we can find the speed:
[tex]Speed = rw\\\\Speed = 0.04 \times 61.24[/tex]
Speed = 2.45 m/s
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