Question

a car of mass 1,270 kg makes a 15.0 m radius turn at 11.8 m/s on flat ground.

how much centripetal force acts on it?

? n

Explanation:

🆕 New Concept Discovered: Centripetal Force
The inward force keeping an object in circular motion

Step 1: Identify the given values

We are given the following values from the problem:

• Mass of the car, \( m = 1,270\text{ kg} \)
• Radius of the turn, \( r = 15.0\text{ m} \)
• Speed of the car, \( v = 11.8\text{ m/s} \)

Step 2: Use the centripetal force formula

Centripetal force is the net inward force required to keep an object moving in a circular path. It is calculated using the formula:

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

Step 3: Calculate the force

Substitute the given values into the formula:

$$ F_c = \frac{1,270 \cdot (11.8)^2}{15.0} $$

First, calculate the square of the speed:

$$ (11.8)^2 = 139.24 $$

Next, multiply by the mass:

$$ 1,270 \cdot 139.24 = 176,834.8 $$

Finally, divide by the radius:

$$ F_c = \frac{176,834.8}{15.0} \approx 11,788.99\text{ N} $$

Rounding to three significant figures (matching the precision of the given values \( 15.0 \) and \( 11.8 \)):

$$ F_c \approx 11,800\text{ N} $$

Answer:

11,800