An air puck of mass 0.382 kg is tied to a string
and allowed to revolve in a circle of radius
0.64 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 0.67 kg
is tied to it. The suspended mass remains in
equilibrium while the puck revolves.
A) What is the tension in the string? The
acceleration due to gravity is 9.8 m/s
2
.
Answer in units of N.
B)What is the horizontal force acting on the
puck?
Answer in units of N.
To find the tension in the string, you can analyze the forces acting on the puck and the suspended mass.
A) The tension in the string is equal to the centripetal force acting on the puck. This force can be calculated using the equation:
Tension = (mass of the puck) × (centripetal acceleration)
The centripetal acceleration can be found using the formula:
Centripetal acceleration = (velocity of puck)^2 / (radius of the circle)
To find the velocity of the puck, you can use the equation:
Velocity = 2π × (radius of the circle) / time period
The time period can be determined using the properties of circular motion.
B) The horizontal force acting on the puck can be found using Newton's second law, which states that Force = mass × acceleration. In this case, the horizontal force is equal to the net force acting on the puck.
The net force can be calculated by considering the forces acting on the puck in the horizontal direction. Since the table is frictionless, the only horizontal force is the tension in the string.
Therefore, the horizontal force acting on the puck is equal to the tension in the string.
To summarize:
A) Tension in the string = (mass of the puck) × (centripetal acceleration)
B) Horizontal force acting on the puck = tension in the string
Now, let's calculate these values using the given information:
mass of the puck (m1) = 0.382 kg
radius of the circle (r) = 0.64 m
mass of the suspended mass (m2) = 0.67 kg
acceleration due to gravity (g) = 9.8 m/s^2
A) To find the tension in the string:
1. Calculate the centripetal acceleration:
Centripetal acceleration = (velocity of puck)^2 / (radius of the circle)
2. Calculate the velocity of the puck:
Velocity = 2π × (radius of the circle) / time period
3. Calculate the time period:
Time period = (2π) × sqrt((m2 + m1) / ((m1 × g)))
4. Calculate the centripetal force:
Centripetal force = (mass of the puck) × (centripetal acceleration)
B) The horizontal force acting on the puck is equal to the tension in the string.
A) To find the tension in the string, we can consider the forces acting on the suspended mass. Since it remains in equilibrium, the tension in the string is equal to the weight of the suspended mass.
The weight of the suspended mass can be calculated using the formula:
Weight = mass * gravity
where mass is 0.67 kg and gravity is 9.8 m/s^2.
Weight = 0.67 kg * 9.8 m/s^2 = 6.586 N
Therefore, the tension in the string is 6.586 N.
B) To find the horizontal force acting on the puck, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Since the puck is moving in a circle of radius 0.64 m on a frictionless table, it experiences centripetal acceleration towards the center of the circle.
The centripetal force acting on the puck can be calculated using the formula:
Centripetal force = mass * (centripetal acceleration)
The centripetal acceleration can be calculated using the formula:
Centripetal acceleration = (linear velocity)^2 / radius
where linear velocity can be calculated using the formula:
Linear velocity = 2 * pi * radius / time period
The time period is the time taken for the puck to complete one revolution, which we do not currently have.
Please provide the time period so that we can calculate the linear velocity, centripetal acceleration, and the horizontal force acting on the puck.