A stone of 400g is whirled by a string of length 2.8m so that it moves in horizontal circle of radius 0.7m.find the tension on the string.
m v^2/r horizontal
m g down
tan theta = mg/(mv^2/R)where theta is angle down from horizontal
but
cos theta = .7/2.8
so theta = 75.5 deg
so tan theta = 3.87
so
3.87 = mg/mv^2/R = 9.81/(v^2/.7)
v = 1.33 m/s
m v^2/R = .4*1.77/.7 = 1.01
m g = .4*9.81 = 3.92
T^2 = 1.01^2 +3.92^2
T = 4.04 N
To find the tension on the string, you can use the centripetal force equation. The centripetal force is the force that keeps an object moving in a circular path and is given as:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the object (400g = 0.4kg)
v is the velocity of the object
r is the radius of the circular path
In this case, the velocity (v) of the object can be determined using the formula:
v = (2 * π * r) / T
Where:
π is the mathematical constant pi (approximately 3.14)
r is the radius of the circular path (0.7m)
T is the time taken to complete one revolution
Given that the object is whirled by a string, we can assume the time taken for one revolution is equal to the period (T) of the circular motion.
To find T, you need to know the speed of the object which can be determined using the length of the string. The speed (v) is given by:
v = 2πr / T
Rearranging the equation:
T = 2πr / v
Now, let's calculate the values step by step:
1. Convert the mass from grams to kilograms:
m = 400g = 0.4kg
2. Calculate the time taken for one revolution (T):
T = 2π(0.7m) / v
3. Calculate the velocity (v):
v = 2π(0.7m) / T
4. Substitute the velocity (v) into the centripetal force equation to find the tension (F):
F = (m * v^2) / r
By following these steps and substituting the appropriate values, you can determine the tension on the string in the given scenario.