An object of mass of 0.5 kg is whirled at the end of a string 0.8 m long.If the string makes three revolutions in 1.2 s,find the tension in the string.
tension=m*g*v^2
v=3*2PI*radius/timefor3revolutions
35.6newton
To find the tension in the string, we can use the centripetal force formula:
F = (m * v^2) / r
where:
F is the centripetal force
m is the mass of the object
v is the velocity of the object
r is the radius of the circular path
In this case, the mass of the object is 0.5 kg and the radius of the circular path is 0.8 m.
To find the velocity of the object, we need to determine the distance the object covers in one revolution. Since the string makes three revolutions in 1.2 seconds, we can divide the total distance covered by the time taken to get the average velocity.
The distance traveled in one revolution is the circumference of the circular path, which is given by:
C = 2πr
In this case, r is 0.8 m. So the circumference is:
C = 2 * 3.14 * 0.8 = 5.02 m
Next, we need to find the time taken for one revolution. Since the string makes three revolutions in 1.2 seconds, the time taken for one revolution is:
t = (1.2 s) / 3 = 0.4 s
Now we can calculate the velocity:
v = distance / time = 5.02 m / 0.4 s = 12.55 m/s
Now we can substitute the values into the centripetal force formula:
F = (0.5 kg * (12.55 m/s)^2) / 0.8 m
Simplifying, we get:
F = 98.84375 N
Therefore, the tension in the string is approximately 98.84 N.