F = ma
To prove this, astronauts on the moon dropped a hammer and a feather on the moon’s surface. Both reached the ground at the same time, because there is no air resistance. Both objects fell with increasing spped. They accelerated at a rate called the acceleration of free fall/ acceleration due to gravity. On earth the acceleration, g is close to 9.8m/s/s.
However, we usually associate the idea with objects dropped vertically, but can F=ma be applied to objects that moves at angle for example on an elevated ramp? But this can’t be done because the theory states that free falling objects fall at a constant acceleration of 9.8m/s/s ONLY if gravity is the only force acting on it. To prove this, I will undergo an experiment involving vectors and mechanics.
Apparatus:
- Toy car
-
Ramp with the length of 1m
- Ramp elevated at an angle of 7.6
Using the idea of vectors, velocity, force, acceleration has a vertical and a horizontal component in order for the object to have a direction. In this case, the car goes down the slope because a force is working on it. The force down the slope, has a vertical component and a horizontal component. On all objects, a gravitional force is pulling objects down , therefore any object has a weight:
Gravitaional force: weight: mass * gravity
To find the components we could attach the horizontal and vertical vectors on to ‘mg’, which forms a right-angle triangle. Unfortunately we can’t use pythagorus theorem because we don’t know the size of each component, even though I know that the mass of the car is o.o655kg, I want to see if I could produce a calculation which will apply to objects regardless of their mass, so I’m going to persume that I do not know the mass.
Using mathematical calculation, I could find one of the angles of the triangle:
I could now find the components by using SOHCAHTOA:
Sin 0= opposite/ hypotenuse = b/mg
Therefore b= sin 0* mg
Cos 0= adjacent/hypotenuse = a/mg
Therefore a=Cos0*mg
To see if this calculation is correct, I’m going to use pythagorus theroem and the knowledge of the car’s mass: 0.0655, and the angle of the elevation: 7.6
(Mg*cosa) + (mg*sinb) = (mg)
(0.065*cos7.6) + (0.0655*sin7.6) = (mg)
(0.06492) + (0.00866) = mg
mg= 0.065 kg and this is correct because the car’s mass was 0.0655, therefore my calculations is right:
The force down the slope would be:
F= mg * sin 0
From Newton’s second law we know that F=ma therefore:
F= mg * sin 0
ma = mg * sin 0 (take mass from both sides0
a=g*sin0 (sin 0 would be a constant)
Therefore, knowing that the angle of eleveation is 7.6:
Acceleration = 9.8 8 sin 7.6
= 1.30 m/s/s
Therefore if the rule of free-falling object was applied to this experiment, acceleration must be 1.30 m/s/s. To see if it does, I’m going to attach a ticker tape to the car and let it go at that angle of elevation, and see whether I get this result.
On a ticker tape, the time to make two dots in 1/50 second, so I’m going to measure the distance between 10 dots, so I’m measuring the displacement every 0.5 s:Using this graph, I can find velocity by finding the gradient of this graph line:
Velocity= displacement/ time = horizontal/vertical =
To find acceleration, we have to find the change in velocity/ time taken, to do this, I could plot a velocity-time graph:
To find acceleration, I need to find the gradient of this graph line.
