Which statement is true about the force of gravity?
1 answer:
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Answer:
N₁ = 393.96 N and N = 197.96 N
Explanation:
In This exercise we must use Newton's second law to find the normal force. Let's use two points the lowest and the highest of the loop
Lowest point, we write Newton's second law n for the y-axis
N -W = m a
where the acceleration is ccentripeta
a = v² / r
N = W + m v² / r
N = mg + mv² / r
we can use energy to find the speed at the bottom of the circle
starting point. Highest point where the ball is released
Em₀ = U = m g h
lowest point. Stop curl down
= K = ½ m v²
Emo = Em_{f}
m g h = ½ m v²
v² = 2 gh
we substitute
N = m (g + 2gh / r)
N = mg (1 + 2h / r)
let's calculate
N₁ = 5 9.8 (1 + 2 17.6 / 5)
N₁ = 393.96 N
headed up
we repeat the calculation in the longest part of the loop
-N -W = - m v₂² / r
N = m v₂² / r - W
N = m (v₂²/r - g)
we seek speed with the conservation of energy
Em₀ = U = m g h
final point. Top of circle with height 2r
= K + U = ½ m v₂² + mg (2r)
Em₀ = Em_{f}
mgh = ½ m v₂² + 2mgr
v₂² = 2 g (h-2r)
we substitute
N = m (2g (h-2r) / r - g)
N = mg (2 (h-r) / r 1) = mg (2h/r -2 -1)
N = mg (2h/r - 3)
N = 5 9.8 (2 17.6 / 5 -3)
N = 197.96 N
Directed down
Answer:
ρ_c < ρ_gold the crown is not gold
Explanation:
For this exercise we use the translational equilibrium condition
∑ F = 0
in the air
T₁ - W = 0
T₁ = W
in water
T + B - W = 0
where T is the scale reading, B the liquid thrust and W the weight
B = W -T
B = 7.84 - 6.84
B = 1 N
thrust is
B = ρ g V_water
V_water =
V_water =
V_water = 1.02 10⁻⁴ m³
how the crown is totally submerged
V_c = V_water
V_c = 1.02 10⁻⁴ m³
now we can calculate the density of the crown
ρ_c = m_c / Vc
W = mg
m = W / g
we substitute
ρ_c =
ρ_c =
ρ_c = 0.784 10⁴ kg / m³
ρ_c = 7.84 10³ kg / m³
We can see that this density is less than the density of gold
ρ_c < ρ_gold
therefore the crown is not gold