A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m),as shown.At an instant when θ = 50°,the tension in the string is 8.0 N.What is the magnitude of the resultant force on the mass at this instant?
A)5.6 N
B)6.0 N
C)6.5 N
D)5.1 N
E)2.2 N

Question

A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m),as shown.At an instant when θ = 50°,the tension in the string is 8.0 N.What is the magnitude of the resultant force on the mass at this instant? 
A)5.6 N 
B)6.0 N 
C)6.5 N 
D)5.1 N 
E)2.2 N

Quizplus · Accepted Answer

At this instant when the tension in the string is 8.0 N, we can use the following equation to calculate the magnitude of the resultant force acting on the mass:

F_res = sqrt((mg)^2 + T^2)

where m is the mass of the object, g is the acceleration due to gravity, and T is the tension in the string.

Substituting the given values, we get:

F_res = sqrt((0.30 kg * 9.81 m/s^2)^2 + (8.0 N)^2)
F_res = sqrt(8.593641 N^2 + 64 N^2)
F_res ≈ 6.5 N  (rounded to one decimal place)

Therefore, the best choice is C), which gives the correct magnitude of the resultant force acting on the mass at that instant.

A 030-Kg Mass Attached to the End of a String Swings