What is the velocity of a 100 g ball on a 50 cm string moving in a horizontal circle that requires a centripetal force of 1 N?

should be 2.24m/s

use the equation F=m(v^2/r)

To find the velocity of a ball moving in a horizontal circle, we need to consider the centripetal force required to keep it in uniform circular motion.

Step 1: Convert mass to kilograms
Given that the mass of the ball is 100 g, we need to convert it to kilograms by dividing it by 1000.
100 g = 100/1000 = 0.1 kg

Step 2: Convert string length to meters
Given that the string length is 50 cm, we need to convert it to meters by dividing it by 100.
50 cm = 50/100 = 0.5 m

Step 3: Find the centripetal force
The centripetal force required to keep an object in uniform circular motion is given by the formula:
Centripetal force (F) = (mass (m) * velocity (v)^2) / radius (r)

We are given that the centripetal force is 1 N, the mass is 0.1 kg, and the radius is 0.5 m.

1 N = (0.1 kg * v^2) / 0.5 m

Step 4: Calculate velocity
Now, let's find the velocity (v).

Rearranging the formula, we have:
v^2 = (F * r) / m

v^2 = (1 N * 0.5 m) / 0.1 kg
v^2 = 0.5 Nm / 0.1 kg
v^2 = 5 Nm/kg

Taking the square root of both sides, we get:
v = √(5 Nm/kg)

Therefore, the velocity of the ball on a 50 cm string, requiring a centripetal force of 1 N, is approximately √(5 Nm/kg).

To find the velocity of the ball, we need to use the centripetal force equation.

The centripetal force (Fc) acting on an object moving in a circle is given by:

Fc = (m * v^2) / r

Where:
- Fc is the centripetal force
- m is the mass of the object
- v is the velocity of the object
- r is the radius of the circle

In this case, the centripetal force is given as 1 N, the mass of the ball (m) is 100 g (which can be converted to kg by dividing by 1000), and the radius (r) is given as 50 cm (which can be converted to meters by dividing by 100).

So, the equation becomes:

1 N = ((100 g) * v^2) / (0.50 m)

Now, we can solve for the velocity (v).

Rearranging the equation, we have:

v^2 = (F * r) / m

Substituting the given values, we get:

v^2 = (1 N * 0.50 m) / (100 g)

Since the mass is in grams, we need to convert it to kilograms:

v^2 = (1 N * 0.50 m) / (0.1 kg)

v^2 = 5 N m / 0.1 kg

Simplifying further, we have:

v^2 = 50 m^2/s^2

Now, to find the velocity (v), we can take the square root of both sides of the equation:

v = √(50 m^2/s^2)

v ≈ 7.07 m/s

Therefore, the velocity of the ball when moving in a horizontal circle with a centripetal force of 1 N is approximately 7.07 m/s.