A metal ball tied to the end of a string 1.8 m long is whirled in a horizontal circle at 4 m/s. What is the mass of the ball if the tension on the string is 30 N?

To find the mass of the ball, we can use the centripetal force equation:

F = (mv^2) / r

where:
F = tension in the string
m = mass of the ball
v = velocity of the ball
r = radius of the circular path

Given:
F = 30 N
v = 4 m/s
r = 1.8 m

Substituting the given values into the equation:

30 = (m * 4^2) / 1.8

Simplifying the equation:

30 = (16m) / 1.8

To isolate the mass, we can multiply both sides of the equation by 1.8:

30 * 1.8 = 16m

Solving for m, we get:

m = (30 * 1.8) / 16

m = 3.75 kg

Therefore, the mass of the ball is approximately 3.75 kg.

To solve this problem, we can use the concept of centripetal force. In circular motion, an object moving in a circle experiences a centripetal force, which is directed towards the center of the circle. The tension in the string provides this centripetal force.

The formula for centripetal force is:

F = (mv^2) / r

Where:
- F is the centripetal force,
- m is the mass of the object,
- v is the velocity of the object, and
- r is the radius of the circle.

In this case, the tension in the string is the centripetal force, F, and it is given as 30 N. The velocity, v, is given as 4 m/s. The radius, r, is given as 1.8 m.

Now, let's rearrange the formula to solve for mass, m:

F = (mv^2) / r

Multiplying both sides of the equation by r:

F * r = mv^2

Now, divide both sides of the equation by v^2:

(F * r) / v^2 = m

Substituting the given values:

m = (30 N * 1.8 m) / (4 m/s)^2

m = (30 N * 1.8 m) / (16 m^2/s^2)

m = 540 Nm / (16 m^2/s^2)

m ≈ 33.75 kg

Therefore, the mass of the ball is approximately 33.75 kg.