A student conducted a series of trials using a rotating mass apparatus to investigate the … — ACT

A student conducted a series of trials using a rotating mass apparatus to investigate the relationship between centripetal force ( $F_c$ ) and the radius of rotation ( $r$ ) for a constant mass moving at a constant speed. The results of the trials are shown in the table below:

Trial	Radius ( $r$ , $\text{m}$ )	Centripetal Force ( $F_c$ , $\text{N}$ )
1	$0.80$	$12.0$
2	$2.40$	?

Given that the centripetal force is inversely proportional to the radius of rotation under these conditions, what is the centripetal force, in newtons, for Trial 2?

Answer: 4 N

Answer

The centripetal force in Trial 2 is

4.0\text{ N}

Since centripetal force is inversely proportional to the radius of rotation, their product must remain constant (

F_c \times r = k

). Using Trial 1, we find

k = 12.0 \times 0.80 = 9.6

. For Trial 2, we set up the equation

F_c \times 2.40 = 9.6

, which yields

F_c = 4.0\text{ N}

Step-by-Step Solution

Identify the mathematical relationship between the variables.

F_c \times r = k

The problem states that centripetal force is inversely proportional to the radius of rotation.

Calculate the constant of proportionality (

k

) using the data from Trial 1.

k = 12.0 \times 0.80 = 9.6

Both the radius (

r = 0.80\text{ m}

) and centripetal force (

F_c = 12.0\text{ N}

) are known for Trial 1.

Calculate the unknown centripetal force for Trial 2.

F_c = \frac{9.6}{2.40} = 4.0

The constant of proportionality is

9.6

and the radius for Trial 2 is

2.40\text{ m}

Key Concept

Inverse Proportionality

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