Answer:
1069.38 gallons
Explanation:
Let V₀ = 1.07 × 10³ be the initial volume of the gasoline at temperature θ₁ = 52 °F. Let V₁ be the volume at θ₂ = 97 °F.
V₁ = V₀(1 + βΔθ) β = coefficient of volume expansion for gasoline = 9.6 × 10⁻⁴ °C⁻¹
Δθ = (5/9)(97°F -52°F) °C = 25 °C.
Let V₂ be its final volume when it cools to 52°F in the tank is
V₂ = V₁(1 - βΔθ) = V₀(1 + βΔθ)(1 - βΔθ) = V₀(1 - [βΔθ]²)
= 1.07 × 10³(1 - [9.6 × 10⁻⁴ °C⁻¹ × 25 °C]²)
= 1.07 × 10³(1 - [0.024]²)
= 1.07 × 10³(1 - 0.000576)
= 1.07 × 10³(0.999424)
= 1069.38 gallons
Answer:
Nutrients the body needs in relatively small amounts are called micronutrients. They include vitamins and minerals. Vitamins are organic compounds that are needed by the body to function properly. ... Vitamins and minerals do not provide energy, but they are still essential for good health
Explanation:
Answer:
a) v = √ 2gL abd b) θ = 45º
Explanation:
a) for this part we use the law of conservation of energy,
Highest starting point
Em₀ = U = mg h
Final point. Lower
Em₂ = ½ m v²
Em₀ = Em₂
m g h = ½ m v²
v = √2g h
v = √ 2gL
b) the definition of power is the relationship between work and time, but work is the product of force by displacement
P = W / t = F. d / t = F. v
If we use Newton's second law, with one axis of the tangential reference system to the trajectory and the other perpendicular, in the direction of the rope, the only force we have to break down is the weight
sin θ = Wt / W
Wt = W sin θ
This force is parallel to the movement and also to the speed, whereby the scalar product is reduced to the ordinary product
P = F v
The equation that describes the pendulum's motion is
θ = θ₀ cos (wt)
Let's replace
P = (W sin θ) θ₀ cos (wt)
P = W θ₀ sint θ cos (wt)
We use the equation of rotational kinematics
θ = wt
P = Wθ₀ sin θ cos θ
Let's use
sin 2θ = 2 sin θ cos θ
P = Wθ₀/2 sin 2θ
This expression is maximum when the sine has a value of one (sin 2θ = 1), which occurs for 90º,
2θ = 90
θ = 45º
