Gravitational Acceleration Problem

In summary, a 95 kg man jumps and exerts a force of 1000 N on a bathroom scale in a motionless elevator in Earth's gravity. Using Newton's 2nd Law, F=ma, the man's acceleration is calculated to be 0.73 m/s^2, taking into consideration the force of gravity. This acceleration is significantly less than the acceleration due to Earth's gravity, as expected from the scale reading of 1000 N.
  • #1
BandGeek13
11
0

Homework Statement


A 95 kg man jumps, therefore exerting a force of 1000 N on a bathroom scale. The scale is in a motionless elevator in Earth's gravity. What is the man's acceleration?


Homework Equations


Newton's 2nd Law: F=ma
Possibly Fg=mg ?


The Attempt at a Solution


I tried just using F=ma.
therefore, it'd be:
1000 N=(95kg)(a)
a=10 m/s^2

But this does not take into consideration the Earth's gravity.
 
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  • #2
Welcome to PF.

"F=ma" uses the net force (vector sum of all forces acting on the man)

Your F uses the 1000N force that the scale exerts on the man. As you suspect, you need to add the force due to Earth's gravity. Just take the vector sum of the scale force and the force due to gravity.
 
  • #3
So would it be:

F(normal)-F(gravity)=ma
F(normal) - mg=ma
1000 N [up] - (95 kg)(9.8 N/kg [down])=(95 kg)(a)
1000 N [up] - 931 N [down] = (95 kg)(a)
69 N [up] = (95 kg)(a)
0.73 m/s^2 = a

This seems very low..
 
  • #4
wait!

instead of:
69 N [up] = (95 kg)(a)
0.73 m/s^2 = a

is it:
1931 N [up] = (95 kg)(a)
20. m/s^2 = a
 
  • #5
BandGeek13 said:
So would it be:
.
.
.
0.73 m/s^2 = a

This seems very low..

Looks good to me.

Note, the man's weight is about 930 N, so the scale would read 930 N when a=0.

The scale reading of 1000N is not much more than this, so expect a to be considerably less than g=9.8 m/s^2.

An acceleration of g=9.8 m/s^2 upward would require a scale reading of 2*930N, which would give Fnet = +930 N upward.

EDIT:
BandGeek13 said:
wait!
.
.
.
is it:
1931 N [up] = (95 kg)(a)
20. m/s^2 = a

Nope. We have +1000N (upward) and -931N (downward), for Fnet=31N upward
 
  • #6
Alright.
Thank you!
 

1. What is gravitational acceleration?

Gravitational acceleration, also known as acceleration due to gravity, is the acceleration that an object experiences due to the gravitational force between it and a larger object, such as the Earth.

2. How is gravitational acceleration calculated?

Gravitational acceleration is calculated using the formula a = GM/r^2, where a is the acceleration, G is the gravitational constant, M is the mass of the larger object, and r is the distance between the two objects.

3. What is the value of gravitational acceleration on Earth?

The value of gravitational acceleration on Earth, denoted as g, is approximately 9.8 m/s^2. However, this value can vary slightly depending on factors such as altitude and latitude.

4. How does gravitational acceleration affect falling objects?

Gravitational acceleration causes falling objects to accelerate towards the Earth at a constant rate. This means that the velocity of a falling object increases by 9.8 m/s every second.

5. How does gravitational acceleration differ on other planets?

Gravitational acceleration on other planets varies depending on the mass and radius of the planet. For example, on Mars, the value of g is approximately 3.7 m/s^2, while on Jupiter, it is approximately 24.8 m/s^2.

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