An air puck of mass 0.102 kg is tied to a string and allowed to revolve in a circle of radius 1.06 m on a horizontal, frictionless table. The other end of the string passes through a hole in the center of the table and a mass of 0.78 kg is tied to it. The suspended mass remains in equilibrium while the puck revolves.
What is the tension in the string? The
acceleration due to gravity is 9.8 m/s
2. Answer in units of N
To find the tension in the string, we can use the concept of centripetal force. In this case, the tension in the string provides the centripetal force required to keep the air puck moving in a circular path.
The centripetal force can be calculated using the formula: Fc = (m * v^2) / r, where Fc is the centripetal force, m is the mass of the air puck, v is its velocity, and r is the radius of the circular path.
Since the air puck remains in equilibrium, we know that the gravitational force acting on the hanging mass is equal in magnitude but opposite in direction to the tension in the string.
The gravitational force can be calculated using the formula: Fg = m * g, where Fg is the gravitational force, m is the mass of the hanging mass, and g is the acceleration due to gravity.
Since the two forces (centripetal force and gravitational force) are equal, we can equate their magnitudes and solve for the tension:
Fc = Fg
(m * v^2) / r = m * g
Now we can substitute the known values into the equation to find the tension:
m = 0.102 kg (mass of the air puck)
v = unknown (velocity)
r = 1.06 m (radius)
g = 9.8 m/s^2 (acceleration due to gravity)
m = 0.78 kg (mass of the hanging mass)
Rearranging the equation, we have:
v^2 = (r * g * m) / m
v = √((r * g * m) / m)
Substituting the given values, we have:
v = √((1.06 m * 9.8 m/s^2 * 0.78 kg) / 0.102 kg)
After calculating the value of v, we can substitute it back into the centripetal force equation to find the tension:
Fc = (m * v^2) / r
Tension = (0.102 kg * v^2) / 1.06 m
To find the answer in units of Newtons, we can simply calculate the value using the given values.
By plugging in the values, we get:
Tension = (0.102 kg * v^2) / 1.06 m
Tension ≈ 10.18 N
Therefore, the tension in the string is approximately 10.18 N.