A 0.300-kg object is swung in a circular path and in a vertical plane on a 0.500-m length string.If the angular speed at the bottom is 4.00 rad/s,what is the tension in the string when the object is at the bottom of the circle?
A) 5.34 N
B) 12.54 N
C) 2.4 N
D) 11.76 N
E) 10.68 N

Question

A 0.300-kg object is swung in a circular path and in a vertical plane on a 0.500-m length string.If the angular speed at the bottom is 4.00 rad/s,what is the tension in the string when the object is at the bottom of the circle?
A) 5.34 N
B) 12.54 N
C) 2.4 N
D) 11.76 N
E) ​10.68 N

Quizplus · Accepted Answer

The tension in the string is given by:$$T = mg + mv^2/r$$where:* m is the mass of the object* g is the acceleration due to gravity* v is the speed of the object* r is the radius of the circleAt the bottom of the circle, the speed of the object is:$$v = rω$$where:* ω is the angular speed of the objectSubstituting this into the equation for tension, we get:$$T = mg + m(rω)^2/r$$$$T = mg + mrω^2$$$$T = (0.300 kg)(9.81 m/s^2) + (0.300 kg)(0.500 m)(4.00 rad/s)^2$$$$T = 5.34 N$$

A 0300-Kg Object Is Swung in a Circular Path and in in a Vertical