how to calculate free fall experiment

• Combined Science
• English Language
• Other Subjects

GCSE Biology

Gcse chemistry, gcse physics, gcse combined science, gcse english language, gcse geography, gcse other subjects.

• Double Science

IGCSE Maths

Igcse biology, igcse chemistry, igcse physics, igcse double science, igcse economics, igcse english language, igcse geography, igcse other subjects, as chemistry, as english language, as other subjects.

• Further Maths

A Level Maths

A level biology, a level chemistry, a level physics, a level english language, a level economics, a level further maths, a level psychology, a level other subjects, o level biology, o level chemistry, o level physics, o level other subjects, pre u maths, pre u biology, pre u chemistry, pre u physics, ib chemistry, ib economics, dp ib physics: sl, revision notes, 2.1.6 acceleration of free fall experiment, acceleration of free fall experiment.

• The acceleration of free fall, g, is defined as:

The acceleration of any object in response to the gravitational attraction between the Earth and the object

• On Earth, the acceleration of free fall is equal to g = 9.81 m s –2

Determining g in the Laboratory

Aims of the experiment.

• The overall aim of the experiment is to calculate the value of the acceleration due to gravity,  g
• The acceleration can then be calculated using an equation of motion
• Independent variable = height, h
• Dependent variable = time, t
• Same steel ball–bearing
• Same electromagnet
• Distance between ball-bearing and top of the glass tube

Equipment List

• Metre ruler = 1 mm
• Timer = 0.01 s

Apparatus setup to measure the distance and time for the ball bearing to drop

This method is an example of the procedure for varying the height the ball-bearing falls and determining the time taken – this is just one possible relationship that can be tested

• Set up the apparatus by attaching the electromagnet to the top of a tall clamp stand. Do not switch on the current till everything is set up
• Place the glass tube directly underneath the electromagnet, leaving space for the ball-bearing. Make sure it faces directly downwards and not at an angle
• Attach both light gates around the glass tube at a starting distance of around 10 cm
• Measure this distance between the two light gates as the height, h with a metre ruler
• Place the cushion directly underneath the end of the glass tube to catch the ball-bearing when it falls through
• Switch the current on the electromagnet and place the ball-bearing directly underneath so it is attracted to it
• Turn the current to the electromagnet off. The ball should drop
• When the ball drops through the first light gate, the timer starts
• When the ball drops through the second light gate, the timer stops
• Read the time on the timer and record this as time, t
• Increase  h (eg. by 5 cm) and repeat the experiment. At least 5 – 10 values for h should be used
• Repeat this method at least 3 times for each value of h and calculate an average t for each
• An example of a table with some possible heights would look like this:

Example Table of Results

Analysis of Results

• The acceleration is found by using one of the SUVAT equations
• Displacement s = h
• Time taken = t
• Initial velocity u = u
• Acceleration a = g
• The following SUVAT equation can be rearranged:

• Substituting in the values and rearranging to fit the straight line equation gives:

• y = 2h/ t (m s – 1 )
• Gradient, m = a =  g  (m s –2 )
• y-intercept = 2 u
• Plot a graph of the 2 h / t against  t
• Draw a line of best fit
• Calculate the gradient - this is the acceleration due to gravity  g
• Assess the uncertainties in the measurements of  h and  t . Carry out any calculations needed to determine the uncertainty in  g due to these

The graph of 2h/t against t produces a straight-line graph where the acceleration is the gradient

Evaluating the Experiment

Systematic Errors:

• Residue magnetism after the electromagnet is switched off may cause t  to be recorded as longer than it should be

Random Errors:

• Large uncertainty in h from using a metre rule with a precision of 1 mm
• Parallax error from reading h
• The ball may not fall accurately down the centre of each light gate
• Random errors are reduced through repeating the experiment for each value of h at least 3-5 times and finding an average time, t

Safety Considerations

• Care must be taken to not have any water near it
• To reduce the risk of electrocution, only switch on the current to the electromagnet once everything is set up
• A cushion or a soft surface must be used to catch the ball-bearing so it doesn’t roll off / damage the surface
• The tall clamp stand needs to be attached to a surface with a G clamp so it stays rigid

Worked Example

Step 1: Complete the table

• Calculate the average time for each height
• Add an extra column 2h / t

Step 2: Draw graph of 2h/t against time t

• Make sure the axes are properly labeled and the line of best fit is drawn with a ruler

Step 3: Calculate the gradient of the graph 

• The gradient is calculated by:

Author: Katie

Quick links.

Requirements

Here is a simulation of the Free Fall apparatus. The drawing is not to scale, and we have also slowed down time.

Free Fall Calculator

Table of contents

This free fall calculator is a tool for finding the velocity of a falling object along with the distance it travels. Thanks to this tool, you can apply the free fall equation for any object, be it an apple you drop or a person skydiving.

Read on to learn the free fall definition and discover the most daring examples, including the highest free fall in history (spoiler alert: it broke the sound barrier )! We'll also explain what free fall acceleration is and why we assume it's constant.

Check out the projectile motion calculator , which describes a case of free fall combined with horizontal motion.

Prefer watching rather than reading? Check out our deep dive into the concept of free fall here:

What is the free fall definition?

In free fall, an object moves under the influence of gravitational force only . The only acceleration is the acceleration of gravity g . No other force, including air resistance, is acting on such an object.

Interestingly, an object in free fall doesn't necessarily need to be falling (that is, moving downwards). For example, the Moon's motion satisfies all of the conditions listed above: there is no other force acting on it other than gravity (it's being pulled towards the Earth), and there is no air resistance, as there is no air in space.

Why doesn't the Moon crash into Earth, then? It's because Moon's speed is not directed towards Earth, but tangentially to its orbit. Since the Moon is moving along an elliptic orbit with a high enough velocity, its motion generates a centrifugal force, equal and opposite to the force of gravity.

You may want to check out our gravitational force calculator and see what an amazing force gravity is.

Free fall speed

From the definition of velocity, we can find the velocity of a falling object is:

• v 0 v_0 v 0 ​ – Initial velocity (measured in m/s or ft/s);
• t t t – Fall time (measured in seconds); and
• g g g – Free fall acceleration (expressed in m/s² or ft/s²).

Without the effect of air resistance, each object in free fall would keep accelerating by 9.80665 m/s (approximately equal to 32.17405 ft/s ) every second. In reality, though, a falling object's velocity is constrained by a value called the terminal velocity .

What is the terminal velocity? As you have seen above, the free-fall acceleration is constant, which means that the gravitational force acting on an object is constant, too. However, the force of air resistance increases with increasing free fall speed. At some point, the two forces become equal in magnitude . According to Newton's first law, at that point, the falling body stops accelerating and moves at a constant speed. This speed is the terminal velocity.

In this free fall calculator, we neglect the influence of air resistance. If you want to consider it, head over to our free fall with air resistance calculator .

Free fall equation

If you want to calculate the distance traveled by a falling object, you need to write down the equation of motion. If the initial displacement and velocity are both equal to zero, it boils down to:

If the object is already traveling with an initial velocity, you have to take it into account, too:

You can immediately see that the object's distance traveled is proportional to the fall time squared. It means that with each second, the falling body travels a substantially larger distance than before.

Another interesting fact is that according to the free fall formula, the distance does not depend on the mass of the falling object . If you drop a feather and a brick, they will hit the ground at the same time… Or at least that's what science says! If you try to perform an experiment, you'll notice that, in reality, the brick falls to the ground first. Why does that happen? Again, because of air resistance. If you dropped the two items in a vacuum, they would both hit the ground at the same instant!

How to use the free fall formula: an example

Still not sure how our free fall calculator works? Don't worry – we prepared a simple example to walk you through it.

Determine the gravitational acceleration. On Earth, this value is equal to 9.80665 m/s² on average (which is also the default value set in the free fall calculator).

Decide whether the object has an initial velocity. We will assume v₀ = 0 m/s .

Choose how long the object is falling. In this example, we will use the time of 8 seconds .

Calculate the final free fall speed (just before hitting the ground) with the formula:

v = v₀ + gt = 0 + 9.80665 × 8 = 78.45 m/s .

Find the free fall distance using the equation:

s = (1/2)gt² = 0.5 × 9.80665 × 8² = 313.8 m .

If you know the height from which the object is falling, but don't know the time of fall, you can use this calculator to find it, too!

Highest free fall in history

You might already have learned the free fall equation, but it's one thing to understand the theory and a completely different one to experience it. There are many ways to experience the thrill of a free fall – you could, for example, jump with a parachute or try bungee jumping!

Technically, such a jump doesn't fulfill all the requirements of a free fall – there is substantial air resistance involved. In fact, a real free fall is only possible in a vacuum. Nevertheless, this is as close to the actual experience as you can get on Earth 😉

One of the most extreme examples of an almost-scientifically correct free fall is the jump of Dr. Alan Eustace, Google's VP of Knowledge, in 2014. Eustace jumped from a heart-stopping height of 135,908 feet (41,425 m) , thus setting a new record for a parachute jump.

Surprisingly, Eustace declined Google's help in the jump and funded the project himself. It was not an easy endeavor because such a leap required him to go up in a special balloon and wear a custom-designed spacesuit that protected him from sudden shifts in temperature (after all, he was jumping from the edge of space). The fall itself took 15 minutes, and the maximum speed exceeded 800 miles per hour – far over the sound barrier!

What is free fall speed?

Why is the weight of a free falling body zero.

It is not. An object in free fall will still have a weight , governed by the equation W = mg , where W is the object’s weight, m is the object’s mass, and g is the acceleration due to gravity. Weight, however, does not affect an object's free-falling speed . Two identically shaped objects weighing a different amount will hit the ground at the same time.

What is the difference between free fall and weightlessness?

Free fall is when an object is falling , only being affected by the force of gravity, while weightlessness is when an object has no weight due to there being no effect from gravity (it still has mass). Weightlessness can be achieved either in space or if an equal force can be applied in the opposite direction of gravity.

How do you find free fall acceleration of a planet?

To find the free fall acceleration of a planet:

Estimate the total mass of the planet in kilograms.

Find the radius of the planet , from its center to its surface, in meters.

Divide the total mass by the radius squared.

Multiply the result by the universal Gravitational constant :

6.67×10 -11 N·m 2 ·kg -2

The result is the gravitational acceleration of the planet, which is also its free-fall acceleration.

Gravitational acceleration (g)

Initial velocity (v₀)

Time of fall (t)

Velocity (v)

Velocity at time t.