Tetherball is a game played by kids. The equipment consists of a volleyball on a string, with the other end of the string tied to the top of a post. Kids hit the ball back and forth around the post. Consider a volleyball of total mass 200 g attached to the top of a post by a 2 m long cord. The volleyball is traveling in a horizontal circle with a speed of 2 m/s. What is the angle θ between the post and the cord in degrees?
30
35.5
25.4
give the correct answer please.........
25.42 to be exact..
25.42
it's 25.42 damn correct.....
25.4
To find the angle θ between the post and the cord, we can use the concept of centripetal force.
The centripetal force is the force that keeps an object moving in a circle. In this case, the tension in the cord provides the centripetal force needed to keep the volleyball moving in the circular path.
The equation for centripetal force is F = mv^2/r, where F is the force, m is the mass of the volleyball, v is the velocity, and r is the radius of the circular path.
In this case, the centripetal force is being provided by the tension in the cord. We can set up an equation with the tension, mass, velocity, and radius:
Tension = mv^2/r
Given:
Mass (m) = 200 g = 0.2 kg
Velocity (v) = 2 m/s
Radius (r) = 2 m
Plugging in the values:
Tension = (0.2 kg)(2 m/s)^2 / 2 m
Simplifying:
Tension = (0.2 kg)(4 m^2/s^2) / 2 m
Tension = 0.4 N
Now, we can analyze the forces acting on the volleyball. There are two forces: the tension in the cord and the force of gravity.
The vertical component of the tension cancels out the force of gravity, as the volleyball is not moving up or down. The horizontal component of the tension provides the centripetal force.
In a right triangle formed by the cord, the horizontal component of the tension is equal to the tension multiplied by the cosine of the angle θ.
Tension (horizontal) = Tension * cos(θ)
Plugging in the value for tension:
0.4 N (horizontal) = 0.4 N * cos(θ)
Now, we can solve for the angle:
cos(θ) = (0.4 N (horizontal)) / (0.4 N)
cos(θ) = 1
θ = arccos(1)
θ = 0 degrees
Therefore, the angle θ between the post and the cord is 0 degrees.