Answer:
9. (B) ¼ Mv²
10. (A) √(3gL)
11. 20 N
12. 5 m/s²
Explanation:
9. The rotational kinetic energy is:
RE = ½ Iω²
RE = ½ (½ MR²) (v/R)²
RE = ¼ Mv²
10. Energy is conserved.
Initial potential energy = rotational energy
mgh = ½ Iω²
Mg(L/2) = ½ (⅓ ML²) ω²
g(L/2) = ½ (⅓ L²) ω²
gL = ⅓ L² ω²
g = ⅓ L ω²
ω² = 3g / L
ω = √(3g / L)
The velocity of the top end is:
v = ωL
v = √(3gL)
11. Sum of torques about the hinge:
∑τ = Iα
-(Mg) (L/2) + (T) (r) = 0
T = MgL / (2r)
T = (3.00 kg) (10 m/s²) (1.60 m) / (2 × 1.20 m)
T = 20 N
12. Sum of forces on the block in the -y direction:
∑F = ma
mg − T = ma
Sum of torques on the pulley:
∑τ = Iα
TR = (½ MR²) (a / R)
T = ½ Ma
Substitute:
mg − ½ Ma = ma
mg = (m + ½ M) a
a = mg / (m + ½ M)
Plug in values:
a = (3.0 kg) (10 m/s²) / (3.0 kg + ½ (6.0 kg))
a = 5 m/s²
A simple electromagnet consisting of a coil of insulated wire wrapped around an iron core<span>. A </span>core<span> of ferromagnetic material like </span>iron<span> serves to increase the magnetic field created. The strength of magnetic field </span>generated<span> is proportional to the amount of </span>current<span> through the winding.</span>
That's <em>TRUE</em>.
For example:
-- When it's Winter in Canada, the USA, and France, it's Summer in Australia, Paraguay, and Namibia. (This is the end of December, all of January and February, and most of March.)
-- When it's Winter in Tasmania, South Africa, and Botswana, it's Summer in Germany, Israel, and Mexico. (This is the end of June, all of July and August, and most of September.)
-- The Spring and Fall are opposite too.