Equation 1
Where V = Velocity, r = radius (see diagram), N = Number of revolutions counted in 60 seconds, t = 60 seconds (length of one trial).
The experimental centripetal force (Fc) of the rubber stopper swinging around is calculated by using:
Equation 2
where ms is the mass of the rubber stopper, and the other variables as before.
Centripetal means “center seeking”. There are two main forces at work in this laboratory exercise. “Opposing” the centripetal force is the theoretical, accepted force due to the weight of the screw nuts pulling the string down through the bottom of the hollow glass tube:
Equation 3
where g = 9.8 m/s2, the accel. due to gravity, and mw is the mass of the screw nuts.
During this experiment, Fc = Fw.. The centripetal force is equal to the weight of the screw nuts.
Procedure:
- The mass of the rubber bund and screw is measured.
- The centripetal force apparatus are constructed as shown above.
- A length of 1m of the nylon string is measured from the rubber bund to the glass tube.
- The length L of the string is marked with the paper marker.
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The glass tube is holded vertically and the rubber bund is whirled around so that the paper marker is just below the glass tuber as shown on the right .
- 50 revolutions of the bung is timed by a partner.
- The angular velocity is calculated.
- The experiment is repeated using different lengths L of the string.
- The results are tabulated.
Data and Data Analysis
Tabulate the results as follows:
Mass of rubber bung m = 0.02609 ± 0.00001 kg
Mass of screw nut M = 0.10135 ± 0.00001 kg
⇒ Tension in string T = Mg = 0.10135 × 9.8 N = 0.99323 N
The string is not horizontal as the rubber bung moves around .In fact , the bung moves in a circle of radius r=Lsinθ.The tension T thus provides both the centipetal force and a force to support the weight of the bung.
By solving T into its horizontal and vertical component,
Tsinθ= mrω2
Tsinθ= m(Lsinθ) ω2
T=mω2L
Mean mω2L = 1.04 N
Error analysis:
Since the measured value of T is larger than the theoretical value m2L there are discrepancies between them. This is because :
(i) there is friction acting at the opening where the string is in contact with the glass tube, causing T is not extactly equal to the weight of the screw nuts ;
(ii) the rubber bung is not whirled with constant speed ;
(iii) the string is not inextensible and
(iv) the rubber bung is not whirled in a horiztonal circle.
(v)the reaction time of the partner
(vi)the length of the string measured is not accurate
Discussion :
1)What are the physical quantities that affect the value of centripetal force when a body in circular motion?
Since T=mω2L , L =r/sinθ
the centripetal force is affected by mass of the object , angular velocity ,the r between the centre of the circle and the object and theθ between the tension and centre or length of the string.
2) What is the force exerted on the object when the object is doing a horizontal circular motion?
The force exerted on the rubber bung include the centripetal force and gravitational pull of the object.
The direction of centripetal force is towards the centre of the circle and the gravitational pull is downward force.
The resultant force is along the string which pointing towards the centre of the circle.
3)What is the weight of the screw nuts in this experiment represents?
Since the tension in one single string is always the same at any point of the string, By T = Mg, the weight of the screw nuts is the tension of the string which equals to the centripetal force acting on the rubber bung.
4)How the forces on the revolving bung and the hanging screw nuts are related?
By solving T=Mg and T=mω2L Mg= T=mω2L
The weight of the screw nuts is equals to the centipetal force acts on the bung which directly proportion to the angular velocity of the bung.
Possible improvements of the experiment:
- The paper mark would sliding during the experiment.Thus highlight pens or marker pens is preferred to use to mark the position instead of paper marker.