How Can We Calculate the Acceleration of Gravity Using Time Measurements?

In summary, the acceleration of gravity can be determined by measuring the time it takes for an object to pass two given points in both directions. If the time it takes to pass a horizontal line A is Ta and the time to pass a second line B is Tb, then the acceleration can be calculated using the formula g = 8h/(Ta^2 - Tb^2), where h is the height between the two parallel lines. This can be derived using the equations of motion for constant acceleration, where the initial velocity and time it takes to pass the lines can be determined.
  • #1
John O' Meara
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The acceleration of gravity can be measured by throwing an object upward and measuring the time that it takes to pass two given points in both directions. Show that the time it takes the object to pass a horizontal line A in both directions is Ta, and the time to pass a second line B in both direction is Tb, then, if acceleration is constant, its magnitude is
g = 8h/(Ta^2 - Tb^2), where h is the height between parallel lines A and B.


V^2=U^2-2gh, V=U+gt; coming down, where U is some unknown initial velocity
V^2+U^2+2gh, V=U-gt; going up

I am a bit rusty as regards the use of the equations of motion for constant acceleration. I have h=(Vb1-Va1)/2g, where Va1 is the velocity the first time the body passes line A on the way up and Vb1 is the vel' the first time the body passes line B on the way up. But I am not sure that I have started on the correct track? I end up with 2h = 2U(Ta1 - Tb1) + g(Tb1^2 - Ta1^2). Where Ta1 is the time the body passed line A (on the way up) and Tb1 is the time the body passed line B (on the way up). It would be great if someone could stat me off. Thanks in advance.
 
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Please see attachment.
 

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  • #3
It is ok I found the same problem in classical physics. Thanks anyway.
 

FAQ: How Can We Calculate the Acceleration of Gravity Using Time Measurements?

What is gravity?

Gravity is a fundamental force of nature that describes the attraction between objects with mass. It is responsible for keeping objects in orbit around larger objects, such as the Earth around the Sun.

How is the acceleration of gravity measured?

The acceleration of gravity, also known as the gravitational acceleration or the gravitational constant, is typically measured using a simple pendulum or a mass on a spring. These objects are affected by the force of gravity and can be used to calculate the acceleration due to gravity.

How does the acceleration of gravity differ on different planets?

The acceleration of gravity on different planets depends on their mass and radius. Generally, the larger the mass and smaller the radius of a planet, the greater its acceleration of gravity will be. For example, the acceleration of gravity on Earth is 9.8 m/s^2, while on the Moon it is only 1.6 m/s^2.

Can the acceleration of gravity change?

The acceleration of gravity is a constant value, meaning it does not change for a given planet or object. However, factors such as altitude, latitude, and the presence of other massive objects can affect the perception of gravity on Earth.

How is the acceleration of gravity related to weight?

The acceleration of gravity and weight are directly proportional to each other. This means that as the acceleration of gravity increases, so does the weight of an object. This is why objects weigh less on the Moon, where the acceleration of gravity is lower, compared to on Earth.

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