Answer:
0.6983 m/s
Explanation:
k = spring constant of the spring = 0.4 N/m
L₀ = Initial length = 11 cm = 0.11 m
L = Final length = 27 cm = 0.27 m
x = stretch in the spring = L - L₀ = 0.27 - 0.11 = 0.16 m
m = mass of the mass attached = 0.021 kg
v = speed of the mass
Using conservation of energy
Kinetic energy of mass = Spring potential energy
(0.5) m v² = (0.5) k x²
m v² = k x²
(0.021) v² = (0.4) (0.16)²
v = 0.6983 m/s
Explanation:
a) 7.5= 111.1×2°= 0.1111×2^3
which can also be written as
(1/2+1/4+1/8+1/16)×8
sign of mantissa:=0
Mantissa(9 bits): 111100000
sign of exponent: 0
Exponent(5 bits): 0011
the final for this is:011110000000011
b) -20.25= -10100.01×2^0= -0.1010001×2^5
sign of mantissa: 1
Mantissa(9 bits): 101000100
sign of exponent: 0
Exponent(5 bits): 00101
the final for this is:1101000100000101
c)-1/64= -.000001×2^0= -0.1×2^{-5}
sign of mantissa: 1
Mantissa(9 bits): 100000000
sign of exponent: 0
Exponent(5 bits): 00101
the final for this is:1100000000100101
Answer:
U_total = 3.51 10⁻¹ J
Explanation:
The electic potential energy is
U = ∑ k 
qi qj / rij
Where k is the Coulomb constant 8.988 109 N m² / C², q are the electric charges and r is the distance between them
Let's apply this equation to our case
Total U = U₁₂ + U₁₃ + U₂₃
The distance between them is the length of the triangle L= 0.3 m, the charge are equal q = 1.40 10⁻⁶ C
U₁₂ = k q₂ / L
All energies are equal for this case, we substitute in the total potential energy
U_total = 3 (k q² / L)
U_total = 6 k q² / L
We calculate
U_total = 6 8,988 10⁹ (1.40 10⁻⁶)² / 0.3
U_total = 3.51 10⁻¹ J
