1) Size of the image: 2 cm
In order to calculate the size of the image, we can use the following proportion:
where
p = 80 m is the distance of the tree from the pinhole
q = 20 cm = 0.2 m is the distance of the image from the pinhole
= 8 m is the heigth of the object
is the height of the image
By re-arranging the proportion, we find
2) Magnification: 0.0025
The magnification of a camera is given by the ratio between the size of the image and the size of the real object:
so, in this problem we have
Answer:
b. 9.5°C
Explanation:
= Mass of ice = 50 g
= Initial temperature of water and Aluminum = 30°C
= Latent heat of fusion = 
= Mass of water = 200 g
= Specific heat of water = 4186 J/kg⋅°C
= Mass of Aluminum = 80 g
= Specific heat of Aluminum = 900 J/kg⋅°C
The equation of the system's heat exchange is given by
The final equilibrium temperature is 9.50022°C
The category of galaxy which does not have a distinctive shape is D. an irregular galaxy.
A spiral galaxy has a spiral shape, an elliptical galaxy has an elliptical shape, and a barred-spiral galaxy has a barred-spiral shape. The only galaxy type which does not have a constant shape is an irregular galaxy.
Answer:
0.191 s
Explanation:
The distance from the center of the cube to the upper corner is r = d/√2.
When the cube is rotated an angle θ, the spring is stretched a distance of r sin θ. The new vertical distance from the center to the corner is r cos θ.
Sum of the torques:
∑τ = Iα
Fr cos θ = Iα
(k r sin θ) r cos θ = Iα
kr² sin θ cos θ = Iα
k (d²/2) sin θ cos θ = Iα
For a cube rotating about its center, I = ⅙ md².
k (d²/2) sin θ cos θ = ⅙ md² α
3k sin θ cos θ = mα
3/2 k sin(2θ) = mα
For small values of θ, sin θ ≈ θ.
3/2 k (2θ) = mα
α = (3k/m) θ
d²θ/dt² = (3k/m) θ
For this differential equation, the coefficient is the square of the angular frequency, ω².
ω² = 3k/m
ω = √(3k/m)
The period is:
T = 2π / ω
T = 2π √(m/(3k))
Given m = 2.50 kg and k = 900 N/m:
T = 2π √(2.50 kg / (3 × 900 N/m))
T = 0.191 s
The period is 0.191 seconds.
Answer:
yes
Explanation:
the force is multiplied by the levers length of the handle
