A 1.0 kg ball is attached to a rigid vertical rod by means of two massless strin
ID: 1769046 • Letter: A
Question
A 1.0 kg ball is attached to a rigid vertical rod by means of two massless strings each 1.0 m long. The strings are attached to the rod at points 1.0 m apart. The system is rotating about the axis of the rod, both string being taut and forming an equilateral triangle with the rod. The tension in the upper string is 25 N. (a) Draw the free-body diagram for the ball. (b) What is the tension in the lower string? (c) What is the net force on the ball at the instant shown in the figure? (d) What is the speed of the ball?Explanation / Answer
use Newton's Second Law. Sketch a Free Body Diagram of the object. There will be a gravitational force mg downward, and a tension force T at an angle up and to the side (let's make it to the left, and let's denote the angle as ? from the vertical). Choose a coordinate system. I strongly recommend that one axis be chosen in the direction of the known acceleration, which is horizontally toward the center (to the left in this case)--be careful, it is NOT in the direction of the tension! I'll call that one the "c" (for center) axis, and I'll let the other axis be "y", upward.
Write out Newton's Second Law (the sum of the forces is ...) for each axis. I'll start with the y axis. Refer to your FBD to get the signs correct (that's why we drew it). I'll show those signs explicitly, so symbols represent magnitudes.
?F_y = T_y - mg = m a_y = 0
where the vertical acceleration of the object is zero.
T_y = T cos?
so
T cos? = mg
Solve for ?.
? = arccos[ mg / T ] = arccos[ (1 kg)(9.81 m/s
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