a stone weighing 0.2kg tied to the end of the string 0.6m long whorld in a horizontal circle in a speed of 150 revolutions per minute. calculte the tension and string
tension=mass*w^2*r
w= 2PI*150/60
To calculate the tension and string in this scenario, we'll need to consider the circular motion of the stone.
First, let's calculate the angular velocity (ω) of the stone. Given that the stone is making 150 revolutions per minute, we need to convert the units to radians per second:
Angular velocity (ω) = (150 revolutions / 1 minute) * (2π radians / 1 revolution) * (1 minute / 60 seconds) = 15π radians/second
Next, we can calculate the centripetal force (Fc) acting on the stone. The centripetal force is given by the formula:
Centripetal force (Fc) = (m * v^2) / r
where m is the mass of the stone, v is the linear velocity, and r is the radius of the circular path.
The linear velocity (v) can be calculated by multiplying the angular velocity (ω) by the radius (r):
Linear velocity (v) = ω * r
In this case, the mass of the stone (m) is 0.2 kg, the angular velocity (ω) is 15π radians/second, and the radius (r) is 0.6 m. Let's sub in these values:
Linear velocity (v) = (15π radians/second) * (0.6 m) = 9π m/s
Finally, we can substitute the values for m, v, and r into the centripetal force formula:
Centripetal force (Fc) = (0.2 kg * (9π m/s)^2) / 0.6 m
Simplifying this equation will give us the tension in the string. Let's do the calculations:
Centripetal force (Fc) = (0.2 kg * (9π m/s)^2) / 0.6 m ≈ 85.75 N
Therefore, the tension in the string is approximately 85.75 Newtons.