Answer:
The angular acceleration of the pencil<em> α = 17 rad·s⁻²</em>
Explanation:
Using Newton's second angular law or torque to find angular acceleration, we get the following expressions:
τ = I α (1)
W r = I α (2)
The weight is that the pencil has is,
sin 10 = r / (L/2)
r = L/2(sin(10))
The shape of the pencil can be approximated to be a cylinder that rotates on one end and therefore its moment of inertia will be:
I = 1/3 M L²
Thus,
mg(L / 2)sin(10) = (1/3 m L²)(α)
α(f) = 3/2(g) / Lsin(10)
α = 3/2(9.8) / 0.150sin(10)
<em> α = 17 rad·s⁻²</em>
Therefore, the angular acceleration of the pencil<em> </em>is<em> 17 rad·s⁻²</em>
<span>-Mass (kg)
-Velocity (m/s)</span>
Answer:
Explanation:
Frictional force acting on the child = μ mg cosθ
, μ is coefficient of kinetic friction , m is mass of child θ is inclination
work done by frictional force
μ mg cosθ x d , d is displacement on inclined plane
work done = .13 x 276 x cos34 x 5.9
= 175.5 J
This work will be converted into heat energy.
b ) Initial energy of child = mgh + 1/2 m v ² , h is height , v is initial velocity
= 276 x 5.9 sin34 + 1/2 x 276 / 9.8 x .518² [ mass m = 276 / g ]
= 910.59 + 3.77
= 914.36 J
loss of energy due to friction = 175.5
Net energy at the bottom
= 738.86 J
If v be the velocity at the bottom
1/2 m v² = 738 .86
.5 x (276 / 9.8) x v² = 738.86
v² = 52.47
v = 7.24 m /s .
Heat
You can usually warm something by adding energy. The added energy can be from light, electricity, friction, a chemical reaction, nuclear reaction, or any other kind of energy. When first added to a substance, energy might be concentrated in one atom, but this one will soon bump into others and spread the energy. Eventually, every atom or molecule in the substance will move a bit faster. When the added energy is spread throughout a substance, it is then called heat energy, thermal energy, or, simply heat. All three terms mean the same thing. Heat is a form of energy, so it has the units of energy. In the SI system, this is Joules. Many other units to measure thermal energy are in common use. Calories and BTU's are common heat units.
Temperature
You cannot measure heat directly, but you can detect its effect on a substance. Changes in heat can usually be detected as changes in temperature. Usually, when you add energy to a bunch of atoms they move faster and get hotter. Similarly, if you remove energy from a bunch of atoms, they usually move less and get cooler.
