A loaded elevator with very worn cables has a total mass of 2600 Kg , and the cables can withstand a maximum tension of 2.90×104 N .
A) Apply Newton's second law to the elevator and find the maximum upward acceleration for the elevator if the cables are not to break?
Take free fall acceleration to be g= 9.80 m/s^2 .
B)What would be the answer to part (a) if the elevator were on the moon, where free fall acceleration is gm = 1.62 m/s^2
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Thank you :)
Tension max = masselevator(g + a)
solve for a.
On the moon? g is 1/6 the g of Earth.
A) Sure, let's apply Newton's second law to the elevator situation. The tension in the cables should be equal to the maximum tension they can withstand, which is given as 2.90×10^4 N. The mass of the elevator is 2600 kg. The downward force on the elevator due to gravity is the mass of the elevator multiplied by the acceleration due to gravity (g).
So, we can set up the equation:
Tension_max = masselevator x (g + a)
Substituting the given values, we get:
2.90×10^4 N = 2600 kg x (9.80 m/s^2 + a)
Now, let's solve for a:
a = (2.90×10^4 N - 2600 kg x 9.80 m/s^2) / 2600 kg
a = (2.90×10^4 N - 25480 N) / 2600 kg
a ≈ 0.427 m/s^2
Therefore, the maximum upward acceleration for the elevator should be approximately 0.427 m/s^2 to prevent the cables from breaking.
B) On the moon, the acceleration due to gravity (gm) is 1.62 m/s^2, which is approximately 1/6th the acceleration due to gravity on Earth. Therefore, in this scenario, the equation will be:
Tension_max = masselevator x (gm + a)
Substituting the given values, we get:
2.90×10^4 N = 2600 kg x (1.62 m/s^2 + a)
We can solve for a again:
a = (2.90×10^4 N - 2600 kg x 1.62 m/s^2) / 2600 kg
a = (2.90×10^4 N - 4212 N) / 2600 kg
a ≈ 0.414 m/s^2
So, in this case, the maximum upward acceleration for the elevator on the Moon would be approximately 0.414 m/s^2.
Hope that helps! Keep reaching for the stars!
A) To find the maximum upward acceleration for the elevator without the cables breaking, we can use Newton's second law.
According to Newton's second law, the net force acting on an object is equal to the product of its mass and acceleration.
Since we want to find the maximum acceleration, we can rearrange the equation as follows:
Tension_max = mass_elevator * (g + a)
Here, Tension_max is the maximum tension the cables can withstand, mass_elevator is the total mass of the elevator, g is the free fall acceleration, and a is the maximum upward acceleration.
To find the maximum acceleration, we need to solve this equation for a:
a = (Tension_max / mass_elevator) - g
Plugging in the given values:
Tension_max = 2.90 × 10^4 N
mass_elevator = 2600 kg
g = 9.8 m/s^2
a = (2.90 × 10^4 N / 2600 kg) - 9.8 m/s^2
Simplifying the equation:
a = 11.15 m/s^2
Therefore, the maximum upward acceleration for the elevator without the cables breaking is 11.15 m/s^2.
B) If the elevator were on the moon, we would need to consider the different value for the free fall acceleration. On the moon, the free fall acceleration (gm) is 1/6 times the free fall acceleration on Earth (g).
So, gm = 1/6 * g = 1/6 * 9.8 m/s^2 = 1.63 m/s^2
Using the same equation as before, but with the new value for gm, we can find the maximum upward acceleration on the moon:
a = (Tension_max / mass_elevator) - gm
Plugging in the given values:
Tension_max = 2.90 × 10^4 N
mass_elevator = 2600 kg
gm = 1.63 m/s^2
a = (2.90 × 10^4 N / 2600 kg) - 1.63 m/s^2
Simplifying the equation:
a = 9.47 m/s^2
Therefore, the maximum upward acceleration for the elevator on the moon, without the cables breaking, would be 9.47 m/s^2.
A) To find the maximum upward acceleration for the elevator if the cables are not to break, we can apply Newton's second law. According to Newton's second law, the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the net force is equal to the tension in the cables, and we want to find the maximum upward acceleration. The tension in the cables can be calculated using the formula:
Tension_max = masselevator * (g + a)
where masselevator is the mass of the elevator and g is the acceleration due to gravity (free fall acceleration), which is 9.80 m/s^2.
To solve for the maximum upward acceleration, we rearrange the formula:
a = (Tension_max - masselevator * g) / masselevator
Substituting the given values:
Tension_max = 2.90 × 10^4 N
masselevator = 2600 kg
g = 9.80 m/s^2
a = (2.90 × 10^4 N - 2600 kg * 9.80 m/s^2) / 2600 kg
Simplifying the equation, we find:
a ≈ 0.705 m/s^2
Therefore, the maximum upward acceleration for the elevator without the cables breaking is approximately 0.705 m/s^2.
B) If the elevator were on the moon, where the free fall acceleration is gm = 1.62 m/s^2, we can use the same equation as in part A, but with the value of g changed to the moon's free fall acceleration.
Substituting the given values:
Tension_max = 2.90 × 10^4 N
masselevator = 2600 kg
g = 1/6 * 9.80 m/s^2 (since the moon's free fall acceleration is 1/6th of Earth's free fall acceleration)
a = (2.90 × 10^4 N - 2600 kg * (1/6 * 9.80 m/s^2) / 2600 kg
Simplifying the equation, we find:
a ≈ 0.260 m/s^2
Therefore, the maximum upward acceleration for the elevator on the moon without the cables breaking is approximately 0.260 m/s^2.