Question

a car of mass 1,180 kg makes a 6.83 m radius turn at 15.2 m/s on flat ground.

how much centripetal force acts on it?

? n

Explanation:

🆕 New Concept Discovered: Centripetal Force
The center-seeking force keeping an object in circular motion

Step 1: Identify the given values

Extract the physical quantities from the problem statement:

• Mass of the car, \( m = 1,180\text{ kg} \)
• Radius of the turn, \( r = 6.83\text{ m} \)
• Velocity of the car, \( v = 15.2\text{ m/s} \)

Step 2: Apply the centripetal force formula

Centripetal force is the net force causing circular motion, directed toward the center of the curve. It is calculated using the formula:

$$ F_c = \frac{m \cdot v^2}{r} $$

Substitute the given values into the equation:

$$ F_c = \frac{1,180 \cdot (15.2)^2}{6.83} $$

Step 3: Calculate the final value

First, calculate the square of the velocity:

$$ (15.2)^2 = 231.04 $$

Next, multiply by the mass:

$$ 1,180 \cdot 231.04 = 272,627.2 $$

Finally, divide by the radius:

$$ F_c = \frac{272,627.2}{6.83} \approx 39,916.13\text{ N} $$

Rounding to three significant figures (matching the precision of the given values like \( 15.2 \) and \( 6.83 \)):

$$ F_c \approx 39,900\text{ N} $$

Answer:

39,900