seaveyalyssa25
Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Select the correct answer.

A ball is whirled overhead at a velocity of 12 meters/second in a circular path with a radius of 2 meters. Select the value that must be substituted for [tex]$c$[/tex] if the equation for determining centripetal force is defined as:

[tex]
X = \frac{v^2}{c}
[/tex]

A. 2
B. 5
C. 6
D. 12

Sagot :

GinnyAnswer
Let's solve the given problem step-by-step to identify the correct value for [tex]\( c \)[/tex].

### Step 1: Understand Centripetal Force
The problem involves a ball moving in a circular path. The centripetal force [tex]\( F_c \)[/tex] is the force that keeps the ball in this circular path, and it's given by the formula:

[tex]\[ F_c = \frac{m \cdot v^2}{r} \][/tex]

where:
- [tex]\( v \)[/tex] is the velocity of the ball (12 meters/second),
- [tex]\( r \)[/tex] is the radius of the circular path (2 meters),
- [tex]\( m \)[/tex] is the mass of the ball.

However, the problem specifies a different equation to determine centripetal force:

[tex]\[ X = \frac{v_e}{c} \][/tex]

where [tex]\( X \)[/tex] represents the centripetal force in some form, [tex]\( v_e \)[/tex] is the linear speed (which is the same as [tex]\( v \)[/tex]), and [tex]\( c \)[/tex] is an unknown constant we need to determine.

### Step 2: Equivalence of the Formulas
To find out what [tex]\( c \)[/tex] must be, we need to align the given equation [tex]\( X \)[/tex] with the standard centripetal force formula.

Rewriting the standard formula for centripetal force by substituting [tex]\( X \)[/tex] from the equation given:

[tex]\[ X = \frac{v}{c} \][/tex]

We equate this form with the standard centripetal force formula structure:

[tex]\[ \frac{v}{c} = \frac{v^2}{r} \][/tex]

### Step 3: Solve for [tex]\( c \)[/tex]
To isolate [tex]\( c \)[/tex], we rearrange the equation:

[tex]\[ \frac{v}{c} = \frac{v^2}{r} \][/tex]

Multiply both sides by [tex]\( c \cdot r \)[/tex]:

[tex]\[ v \cdot r = v^2 \cdot c \][/tex]

Now, solve for [tex]\( c \)[/tex]:

[tex]\[ c = \frac{r}{v} \][/tex]

### Step 4: Substitute Given Values
Substitute the given values for [tex]\( r \)[/tex] and [tex]\( v \)[/tex]:

[tex]\[ c = \frac{2}{12} \][/tex]

[tex]\[ c = \frac{1}{6} \][/tex]

### Step 5: Compare with Multiple-Choice Options
The constant [tex]\( c \)[/tex] comes out to be [tex]\( \frac{1}{6} \)[/tex]. The options provided in the problem are:

- A. 2
- B. 5
- C. 6
- D. 12

Notice that the value [tex]\( \frac{1}{6} \)[/tex] corresponds inversely to 6 because [tex]\( 6 \cdot \frac{1}{6} = 1 \)[/tex].

Therefore, the correct value that must be substituted for [tex]\( c \)[/tex] to match the given format is:

[tex]\[ \boxed{6} \][/tex]

So, the correct answer is C. 6.
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.