Question Part
Points
Submissions Used
1 2 3
3/3 0/2 0/5
3/10 1/10 1/10
Total
3/10
Consider a conical pendulum with a 90.0 kg bob on a 10.0 m wire making an angle of θ = 3.00° with the vertical. (Consider + to be towards the center of the circular path.)
(a) Determine the horizontal and vertical components of the force exerted by the wire on the pendulum.
N +
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N
(b) What is the radial acceleration of the bob?
To determine the horizontal and vertical components of the force exerted by the wire on the pendulum, we need to decompose the gravitational force acting on the bob into its horizontal and vertical components.
(a) The gravitational force acting on the bob can be calculated using the formula Fg = mg, where m is the mass of the bob and g is the acceleration due to gravity. In this case, m = 90.0 kg and g = 9.8 m/s^2.
Fg = (90.0 kg)(9.8 m/s^2) = 882 N
The horizontal component of the force exerted by the wire can be found using the formula Fx = Fg * sin(θ), where θ is the angle between the wire and the vertical.
Fx = 882 N * sin(3.00°) = 45.9 N
Therefore, the horizontal component of the force exerted by the wire is 45.9 N.
The vertical component of the force exerted by the wire can be found using the formula Fy = Fg * cos(θ), where θ is the angle between the wire and the vertical.
Fy = 882 N * cos(3.00°) = 881.7 N
Therefore, the vertical component of the force exerted by the wire is 881.7 N.
(b) The radial acceleration of the bob can be calculated using the formula ar = (v^2) / r, where v is the magnitude of the velocity of the bob and r is the radius of the circular path.
In a conical pendulum, the velocity of the bob can be found using v = √(gr * tan(θ)), where g is the acceleration due to gravity and θ is the angle between the wire and the vertical.
v = √((9.8 m/s^2) * (10.0 m) * tan(3.00°) = 9.92 m/s
The radius of the circular path is the length of the wire.
r = 10.0 m
Using these values in the formula, we can calculate the radial acceleration.
ar = (9.92 m/s)^2 / 10.0 m = 9.82 m/s^2
Therefore, the radial acceleration of the bob is 9.82 m/s^2.