if a 40.0-g stone is whirled horizontally on the end of a 0.60-mstring at a speed of 22m/s what is the tension in the string?
To calculate the tension in the string, we need to consider the forces acting on the stone. In this case, the stone is being whirled horizontally, which means there are two forces acting on it: the tension force provided by the string and the gravitational force pulling the stone downward.
To find the tension in the string, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
First, let's find the acceleration of the stone. Since the stone is moving in a circle, it experiences centripetal acceleration directed toward the center of the circle. The centripetal acceleration can be calculated using the following equation:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity
r = radius of the circular path
In this case, the velocity (v) is given as 22 m/s, and the radius (r) is given as 0.60 m. Plugging these values into the equation gives us:
a = (22 m/s)^2 / 0.60 m
Next, we can calculate the centripetal force acting on the stone, which is equal to the tension in the string. The centripetal force can be calculated using the following equation:
F = m * a
Where:
F = centripetal force (tension in the string)
m = mass of the stone
a = centripetal acceleration
In this case, the mass (m) is given as 40.0 g, which we can convert to kilograms by dividing by 1000. Plugging in the values for mass (m) and centripetal acceleration (a) gives us:
F = (40.0 g / 1000 kg/g) * (22 m/s)^2 / 0.60 m
Evaluating this expression gives us the tension in the string.