Acceleration, Force and Mass

... . From this you can tell something about the proportionality between the other two factors, the force and the acceleration. That is that they are proportional, and this is stated in Newton's laws of motion. You can tell proportionality on a graph because of two features:

1.The graph is a straight line 2. The line goes straight through the origin

We also know that when the graph has been drawn we will be able to take the gradient of the line. This gradient should be equal to

mass of the trolley:

F = ka

k = F / a

(k is an unknown constant, in this case the mass of

the trolley or the gradient)

If we were to keep the same force acting on the trolley, but to change the mass each time, this is what we might expect.

m = F / a ; m = k / a ; m 1 / a

This tells you that the mass of the trolley will be proportional to inversion of the acceleration (1 / a). Yet again the graph of this will be a straight line through the origin. From this, if you took the gradient of the graph mass against 1 / acceleration then the gradient will be the 1 / Force acting on the trolley. Here is how we know this:

m 1 / a ; gradient = 1 / a = 1 / F

m

Overall I state that when Force is plotted against acceleration then the graph will be directly proportional. Then if I take the gradient of the graph then it should equal the mass of the trolley. On the other hand I will only be able to speculate from my results what will happen when the force is remaining constant as it will not be possible to have a range of masses to do the experiment with, and the force is what I have stated I am changing each time!

Results:

Mass /kg (trolley)

Force /N

(force applied)

Distance

1

/m

Velocity1

/m/s

Distance

2

/m

Velocity2

/m/s

Acceleration

/m/s²

Average

Acceleration

/m/s²

0.775

0.5

0.021

0.022

0.021

0.105

0.110

0.105

0.034

0.036

0.034

0.170

0.180

0.170

0.325

0.350

0.325

0.333

0.775

1.0

0.031

0.033

0.032

0.155

0.165

0.160

0.062

0.065

0.063

0.310

0.325

0.315

0.775

0.800

0.775

0.783

0.775

1.5

0.041

0.043

0.045

0.205

0.215

0.225

0.082

0.082

0.080

0.410

0.405

0.400

1.025

0.950

0.875

0.950

0.775

2.0

0.056

0.058

0.055

0.280

0.290

0.245

0.112

0.114

0.113

0.560

0.580

0.565

1.400

1.450

1.450

1.433

0.775

2.5

0.064

0.064

0.063

0.320

0.320

0.315

0.120

0.125

0.123

0.600

0.625

0.615

1.400

1.525

1.500

1.475

0.775

3.0

0.072

0.071

0.070

0.360

0.355

0.350

0.144

0.141

0.140

0.720

0.705

0.700

1.800

1.750

1.750

1.766 ...