Investigating Force, Mass and Acceleration using a Trolley

Aim of experiment:

Using simple trolley experiments, take suitable measurements from them to find the Mass of the trolley, the fraction force acting in the system and to investigate any other effects found when using apparatus.

Let M = the mass of the trolley (A), MA = Mass added onto the trolley

MB = the mass of the hanging mass (B)

t = Tension in the string

g = Gravitational force = 9.8 N

R = the resistive force acting in the system.

i.e. Fraction between the track and the trolley, fraction force in the pulley and air resistance.

The Diagram above shows the setup of apparatus for the particular experiments. The acceleration meter measures the acceleration of the system by measuring the time taken through each of the 4cm cardboard and the time interval (t) between the two cardboards. The speed (u, v) through each of them is calculated and the acceleration is calculated using the formulae.

a = (v - u)/ t

Two sets of experiments are carried out:

First experiment:

0.09 kg of mass (MA) is placed on the trolley and the hanging mass (MB) is 0.01 kg at the start. The acceleration of the system is measured. Then 0.01 kg of mass is taken from the trolley each time and added to the hanging mass and acceleration of the system is measured. The experiment is carried on as the same procedure until MA = 0 kg and MB = 0.1 kg

In this case MA + MB is always equal to 0.1 kg and the mass of the system is always equals to MA + MB + M = (M + 0.1) kg

Using F - R = ma where a = acceleration, m = mass

Acceleration of A: t - R = (M + MA)a

B: MBg - t = MB a MBg - MB a = t

? MBg - MB a - R = (M + MA)a

MBg - R = a (M +MA + MB)

a = (MBg - R) / (M + MA + MB)

a = (MBg - R) / (M + 0.1)

Aim of experiment:

Using simple trolley experiments, take suitable measurements from them to find the Mass of the trolley, the fraction force acting in the system and to investigate any other effects found when using apparatus.

Let M = the mass of the trolley (A), MA = Mass added onto the trolley

MB = the mass of the hanging mass (B)

t = Tension in the string

g = Gravitational force = 9.8 N

R = the resistive force acting in the system.

i.e. Fraction between the track and the trolley, fraction force in the pulley and air resistance.

The Diagram above shows the setup of apparatus for the particular experiments. The acceleration meter measures the acceleration of the system by measuring the time taken through each of the 4cm cardboard and the time interval (t) between the two cardboards. The speed (u, v) through each of them is calculated and the acceleration is calculated using the formulae.

a = (v - u)/ t

Two sets of experiments are carried out:

First experiment:

0.09 kg of mass (MA) is placed on the trolley and the hanging mass (MB) is 0.01 kg at the start. The acceleration of the system is measured. Then 0.01 kg of mass is taken from the trolley each time and added to the hanging mass and acceleration of the system is measured. The experiment is carried on as the same procedure until MA = 0 kg and MB = 0.1 kg

In this case MA + MB is always equal to 0.1 kg and the mass of the system is always equals to MA + MB + M = (M + 0.1) kg

Using F - R = ma where a = acceleration, m = mass

Acceleration of A: t - R = (M + MA)a

B: MBg - t = MB a MBg - MB a = t

? MBg - MB a - R = (M + MA)a

MBg - R = a (M +MA + MB)

a = (MBg - R) / (M + MA + MB)

a = (MBg - R) / (M + 0.1)