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 ?
The tension in the string provides the centripetal force that keeps the ball moving in a circle. We can use the centripetal force formula to find the mass of the ball.
The centripetal force (F) is given by the equation:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the ball
v is the velocity of the ball
r is the radius of the circle
Given:
v = 4 m/s
r = 1.8 m
F = 30 N
Let's rearrange the formula to solve for the mass (m):
m = (F * r) / v^2
m = (30 N * 1.8 m) / (4 m/s)^2
m = 54 N*m / 16 m^2/s^2
m ≈ 3.375 kg
Therefore, the mass of the ball is approximately 3.375 kg.
To find the mass of the ball, we can start by analyzing the forces acting on it. In this scenario, the tension in the string provides the centripetal force necessary to keep the ball moving in a circular path.
The centripetal force (F) can be calculated using the following formula:
F = (m * v^2) / r
Where:
F = Centripetal force
m = Mass of the ball
v = Velocity of the ball
r = Radius of the circular path
In this case, the centripetal force is equal to the tension in the string, which is given as 30 N. The velocity of the ball is 4 m/s, and the length of the string (radius) is 1.8 m.
We can rearrange the formula to solve for the mass (m):
m = (F * r) / v^2
Plugging in the values:
m = (30 N * 1.8 m) / (4 m/s)^2
Now, let's calculate it step by step:
Step 1: Calculate the square of the velocity:
v^2 = (4 m/s)^2
v^2 = 16 m^2/s^2
Step 2: Multiply the tension (F) by the radius (r):
F * r = 30 N * 1.8 m
F * r = 54 N·m
Step 3: Divide the result of step 2 by the result of step 1 to get the mass (m):
m = (54 N·m) / (16 m^2/s^2)
Step 4: Simplify the expression:
m = 3.375 kg
Therefore, the mass of the ball is approximately 3.375 kg.