Finding Acceleration Due To Gravity

In summary, a Gak living on a planet in another galaxy drops a ball with a mass of 4.88 kg and notes that it takes 0.712 s to fall a distance of 4.04 m. Using the formula d = vt + (1/2)at2, the acceleration due to gravity on the Gak's planet is found to be 3.98 ms^-2. However, the given method to find the speed is incorrect and a different formula should be used.
  • #1
Dave Johnson
8
0

Homework Statement


A Gak it a type of alien that lives on a planet in another galaxy. One day a Gak decides to find out a little more about his planet. He drops a ball (it starts at rest) with a mass of 4.88 kg and notes that it takes 0.712 s to fall a distance of 4.04 m.

What is the acceleration due to gravity on the Gak’s planet?

Homework Equations


mgh = 0.5mv^2

The Attempt at a Solution


V = 4.04/0.712 = 5.67m/s
g = (0.5V^2)/h = [0.5(5.67)^2]/4.04 = 3.98ms^-2

However, answer is incorrect. Can someone kindly help me please?
 
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  • #2
Your method of getting v is wrong. It only gives you the average speed. The instantaneous speed of the ball is changing all the time, as it falls. You should be able to use a formula which does not involve the speed, but involves only the quantities for which the data is given.
 
  • #3
I see... But i can't seem to find any formula without any given radius.
 
  • #4
Sorry. What is the radius we are talking about here?
 
  • #5
the formula for acceleration due to gravity is g = G*M/R^2. R is the radius
 
  • #6
But the data for the radius and mass are not given. So how do you use that?
 
  • #7
Yap that why i said its hard to solve this question without radius.
 
  • #8
Can you think of a formula that connects the distance the ball drops to time?
 
  • #9
d = vt + (1/2)at2?
 
  • #10
What is v in your formula?
 
  • #11
0
 
  • #12
So now you can find g, right?
 
  • #13
yap cheers
 

Related to Finding Acceleration Due To Gravity

What is acceleration due to gravity?

Acceleration due to gravity is the rate at which an object falls towards the ground when dropped in a vacuum. It is typically denoted by the symbol "g" and has a constant value of approximately 9.8 meters per second squared on Earth.

How do you calculate acceleration due to gravity?

To calculate acceleration due to gravity, you can use the formula g = GM/r^2, where G is the gravitational constant (6.67x10^-11 N*m^2/kg^2), M is the mass of the larger object (such as Earth), and r is the distance between the two objects (such as the radius of Earth).

Why does acceleration due to gravity vary on different planets?

The acceleration due to gravity varies on different planets because it is dependent on the mass and radius of the planet. For example, Jupiter has a much larger mass and radius than Earth, resulting in a stronger gravitational force and a higher acceleration due to gravity.

How is acceleration due to gravity measured?

Acceleration due to gravity can be measured using a variety of methods, such as dropping an object and measuring its fall time or using a pendulum and measuring its period. These measurements can then be used to calculate the acceleration due to gravity using the formula g = 2πL/T^2, where L is the length of the pendulum and T is the period of its swing.

Can acceleration due to gravity be negative?

Technically, acceleration due to gravity can be negative if it is directed downwards (towards the center of the Earth). However, it is typically expressed as a positive value since gravity is always acting downwards and objects are always accelerating towards the ground due to gravity.

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