Please, I need help with this problem. I would really appreciate it.
The top of Mt. Everest is 8850 m above sea level. Assume that sea level is at the average Earth radius of 6.38×106 m. What is the magnitude of the gravitational acceleration at the top of Mt. Everest? The mass of the Earth is 5.97×1024 kg.
Answer:__________ m/s^2
Thank you.
I just did this for someone a few minutes ago.
Posted by Kathy on Sunday, April 21, 2013 at 6:37pm.
Could anyone please help me with this problem? I would really appreciate it.
The top of Mt. Everest is 8850 m above sea level. Assume that sea level is at the average Earth radius of 6.38×106 m. What is the magnitude of the gravitational acceleration at the top of Mt. Everest? The mass of the Earth is 5.97×1024 kg.
Answer ________ N
Thank you.
physics (Newton - Damon, Sunday, April 21, 2013 at 6:52pm
F = G m M / r^2
a = F/m
a = G M/r^2
a = 6.67*10^-11 (5.97*10^24) / (6,380,000+8,850)^2
a = (6.67*5.97/4.08)10^(-11+24-13)
a = 9.76 * 10^0
= 9.76 m/s^2
Hey, look for answers already posted.
To find the magnitude of the gravitational acceleration at the top of Mt. Everest, we can use the formula for gravitational acceleration:
g = (G * M) / (r^2)
where:
- g is the gravitational acceleration
- G is the gravitational constant, approximately 6.67430 × 10^-11 N(m/kg)^2
- M is the mass of the Earth
- r is the distance between the center of the Earth and the top of Mt. Everest
First, let's convert the average Earth radius from meters to kilometers:
average Earth radius = 6.38 × 10^6 m = 6380 km
Next, we need to find the distance between the top of Mt. Everest and the center of the Earth. Since the height of Mt. Everest is given as 8850 m above sea level, we can calculate the distance as:
distance = average Earth radius + height of Mt. Everest
distance = 6.38 × 10^6 m + 8850 m
Now that we have the distance (r) between the top of Mt. Everest and the center of the Earth, we can substitute the values into the formula for gravitational acceleration:
g = (6.67430 × 10^-11 N(m/kg)^2 * 5.97 × 10^24 kg) / ((6.38 × 10^6 m + 8850 m)^2)
Now, let's calculate the magnitude of the gravitational acceleration at the top of Mt. Everest by plugging in the values and performing the calculation using a calculator:
g ≈ (6.67430 × 10^-11 N(m/kg)^2 * 5.97 × 10^24 kg) / ((6.38 × 10^6 m + 8850 m)^2)
After performing the calculations, you should get an answer of approximately 9.772 m/s^2 for the magnitude of the gravitational acceleration at the top of Mt. Everest.