Circular and Satellite Motion - Mission CG5 Detailed Help

A 2.32-kg bucket of water is suspended from a string and swung in a horizontal circle, making 10 revolutions in 8.63 seconds. The radius of the circle is 0.945 meters. Determine the velocity (in m/s), acceleration (in m/s/s), the net force (in N) and the magnitudes of all individual forces. (Note that the tension force has been resolved into horizontal and vertical components.) Finally, indicate the direction of the net force and acceleration ... .

(Note: Your numbers are randomly selected and may differ from the numbers listed above.)


 
Detail #1: Many students quickly reach a standstill on the questions in this mission because they fail to click on the Direction button for acceleration and net force in order to toggle to the correct direction. Since this is central to the solution, you might do it first.
 
Detail #2: Minds on Physics calculates answers to the fourth decimal place. Your answers do not need to be that accurate. To be safe, enter at least four digits on each answer. If doing a sequence of consecutive calculations, do not round intermediate values; save all rounding until the final value has been determined. 


 
Often times, success in physics demands that you have the proper approach - a good game plan. The following strategy should serve you well:
  1. Read the physical situation, analyze the diagram and determine the direction of the net force and acceleration. Click on the Dir'n button to set the direction to inward.
  2. Determine the speed of the bucket from knowledge of the R and the time. The speed is the ratio of distance to time. The bucket makes 10 circumferences in 8.63 seconds. A circumference has a distance of 2•PI•R. If necessary, see Formula Frenzy section.
  3. Determine the acceleration of the bucket from the knowledge of v and R. If necessary, see Formula Frenzy section.
  4. Determine the net force on the bucket from the knowledge of m and a. If necessary, see Formula Frenzysection.
  5. Since there is no up-down acceleration, the gravity force and the y-component of the tension force (Fy) must balance each other. Determine the gravity force from the mass. If necessary, see Formula Frenzy section. Then determine the y-component.
  6. The net force on the bucket is supplied by the x-component of the tension force (Fx). Thus, the x-component is equal to the net force.

All blanks should now be filled in. Check your answer. If there is a mistake, recheck your calculations and try again. Be cautious of the rounding of answers.



 
The speed (v) of an object moving in a circle can be determined from knowledge of the radius of the circle (R) and the period (T) or time to complete a cycle around the circle. The relationship is expressed by the equation:
v = 2 • PI • R / T


The acceleration (a) of an object moving in a circle is dependent upon the speed (v) of the object and the radius (R) of the circle. The relationship is expressed by the equation:
 
a = v2 / R


The weight of an object or gravitational force (Fgrav) is dependent upon the object's mass (m) and the acceleration of gravity (g) - 9.8 m/s/s. The relationship is expressed by the equation:   

Fgrav = m • g


The net force (Fnet) acting on an object is dependent upon the object's mass (m) and its acceleration (a). The relationship is expressed by the equation: 

Fnet = m • a