55 J
Explanation:
Kinetic energy is given as: 0.5MV^2 where M is the mass and V is the speed of rotation. Since the masses are point masses, we calculate the point mass for each mass.
M1 = 30*0.2^2 = 1.2kgm^2
M2 = 20*0.4^2 = 3.2kgm^2
V = 5 rad/s
Calculating using the formula above, we obtain :
0.5(1.2+3.2)5^2 =0.5*4.4*25 = 55 J
Answer:
4.4×10⁻⁷ Coulomb
Explanation:
V = Voltage = 5.8 kV
d = Potential distance = 2.8 mm = 0.0028 m
A = Area = 0.3×0.08 = 0.024 m²
ε₀ = permittivity constant in a Vacuum= 8.85×10⁻¹² F/m
Magnitude of charge transferred between a carpet and a shoe is 4.4×10⁻⁷ Coulomb.
The kinds of atoms in the substance and their arrangements
Recall the definition of the cross product with respect to the unit vectors:
i × i = j × j = k × k = 0
i × j = k
j × k = i
k × i = j
and that the product is anticommutative, so that for any two vectors u and v, we have u × v = - (v × u). (This essentially takes care of part (b).)
Now, given a = 8i + j - 2k and b = 5i - 3j + k, we have
a × b = (8i + j - 2k) × (5i - 3j + k)
a × b = 40 (i × i) + 5 (j × i) - 10 (k × i)
… … … … - 24 (i × j) - 3 (j × j) + 6 (k × j)
… … … … + 8 (i × k) + (j × k) - 2 (k × k)
a × b = - 5 (i × j) - 10 (k × i) - 24 (i × j) - 6 (j × k) - 8 (k × i) + (j × k)
a × b = - 5k - 10j - 24k - 6i - 8j + i
a × b = -5i - 18j - 29k
