Answer:
K_{total} = 19.4 J
Explanation:
The total kinetic energy that is formed by the linear part and the rotational part is requested
let's look for each energy
linear
= ½ m v²
rotation
= ½ I w²
the moment of inertia of a solid sphere is
I = 2/5 m r²
we substitute
= ½ mv² + ½ I w²
angular and linear velocity are related
v = w r
we substitute
K_{total} = ½ m w² r² + ½ (2/5 m r²) w²
K_{total} = m w² r² (½ + 1/5)
K_{total} = 
m w² r²
let's calculate
K_{total} = 6.40 16.0² 0.130²
K_{total} = 19.4 J
Answer
-8.67× 10^6 N/C
Explanation:
The Electric Field is defined as force per unit charge.
E = Q/ 4π£r2
Qv= −6.5 μCm3
Qv = Q/ V= Q/ 4/3 πr3
Hence Q = 4/3 πr3 × Qv
Hence E = 4/3 πr3 × Qv / 4π£r2= Qvr/3£
−6.5 μ × 4/ 3×8.854 ×10^-12
-6.5 × 4 × 10^6/3 = -8.67× 10^6 N/C
Note: £ = 8.854×10^-12m/F
is the permittivity of free space
Qv is the charge per unit volume
V is volume and volume
Answer:
a = 16 m/s²
General Formulas and Concepts:
<u>Dynamics</u>
Newton's Law of Motions
- Newton's 1st Law of Motion: An object at rest remains at rest and an object in motion stays in motion
- Newton's 2nd Law of Motion: F = ma (Force is equal to [constant] mass times acceleration)
- Newton's 3rd Law of Motion: For every action, there is an equal and opposite reaction<u>
</u>
Explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
[Given] F = 22000 N
[Given] m = 1375 kg
[Solve] a
<u>Step 2: Find Acceleration</u>
- Substitute in variables [Newton's 2nd Law of Motion]: 22000 N = (1375 kg)a
- Isolate <em>a</em>: 16 m/s² = a
- Rewrite: a = 16 m/s²
The distance between a trough and a crest is double the amplitude.
The distance between trough and crest is (9m - 6m) = 3m.
So the amplitude of those water waves is (3/2) = 1.5 meters.
For this question, we really don't need to know how far apart the crests are, or how often they pass. There may be more parts to the question, for which that information is needed.
For example:
-- What's the wavelength of the waves ? 8 meters.
-- What's the period of the waves ? 4 seconds.
-- What's the frequency of the waves ? 1 / (4 seconds) = 0.25 Hz.
-- What's the speed of the waves ? (8 m) x (0.25 Hz) = 2 m/s
By conservation of linear amount of movement, we have to
p1 = p2
Where, p = m * v.
So, using the definition for this case, we have:
(2.9 kg)•(26 cm/s) = (2.1 kg + 2.9 kg)•v
75.4 kg•cm/s = (5.0 kg)•v
v = 15.1 cm/s
