A trip is taken that passes through the following points in order
1 answer:
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Answer:
A) v = 1,675 10³ m / s , B) r₂ = 11,673 10⁶ m
Explanation:
A) This exercise we must use Newton's second law, where the forces of gravity are the Moon
F = m a
acceleration is centripetal
a = v² / r
force is the force of universal attraction
F = G m M / r²
we substitute
G m M / r² = m v² / r
v² = G M / r
distance
r = R_moon + h
r = 1.74 10⁶ +1.0786 10⁴
r = 1,750786 10⁶ m
we calculate
v = √ (6.67 10⁻¹¹ 7.36 10²² / 1.75 10⁶)
v = √ (2,8052 10⁶)
v = 1,675 10³ m / s
B) let's use energy conservation
Starting point. In the mountain
Em₀ = K + U = ½ m v² + G m M / r
Final point. Where the speed is zero
= U = G mM / r₂
Em₀ = Em_{f}
½ m v² + G m M / r = G mM / r₂
1 / r₂ = (½ v₂ + G M / r) / GM
let's calculate
1 / r₂ = (½ (1,675 10³)² + 6.67 10⁻¹¹ 7.36 10²² / 1.75 10⁶) /(6.67 10⁻¹¹ 7.36 10²²)
1 / r₂ = (1,4028 10⁶ + 2,805 10⁶) / 49.12 10¹¹
1 / r₂ = 8.5664 10⁻⁷
r₂ = 11,673 10⁶ m
Answer:
8.9
Explanation:
We can start by calculating the initial elastic potential energy of the spring. This is given by:
(1)
where
k = 35.0 N/m is the initial spring constant
x = 0.375 m is the compression of the spring
Solving the equation,
Later, the professor told the student that he needs an elastic potential energy of
U' = 22.0 J
to achieve his goal. Assuming that the compression of the spring will remain the same, this means that we can calculate the new spring constant that is needed to achieve this energy, by solving eq.(1) for k:
Therefore, Tom needs to increase the spring constant by a factor: