The horizontal surface on which the objects slide is frictionless. If F = 12 N, what is the tension in string 1?
A)35 N
B)30 N
C)40 N
D)45 N
E)25 N

Question

The horizontal surface on which the objects slide is frictionless. If F = 12 N, what is the tension in string 1? 
A)35 N 
B)30 N 
C)40 N 
D)45 N 
E)25 N

Quizplus · Accepted Answer

Since the surface is frictionless, the tension in string 2 is also 12N. Therefore, the tension in string 1, which acts in the opposite direction, must also be 12N. However, since the 3 kg block is being lifted, we need to add the weight force (mass x gravity) of the block, which is 3 kg x 9.8 m/s^2 = 29.4N. Therefore, the total tension in string 1 is 12N + 29.4N = 41.4N. But, string 1 is at an angle of 30 degrees, so we need to resolve the tension force into its vertical and horizontal components using trigonometry. The vertical component is T cos(30) and the horizontal component is T sin(30). Since the block is being lifted vertically, we need to equate the weight force to the vertical component of tension. Therefore, T cos(30) = 29.4N, which means T = 29.4N / cos(30) = 34.0N. However, the question asks for the tension in string 1, not the total tension. Since the tension in string 2 is 12N, the tension in string 1 is T - 12N = 34.0N - 12N = 22.0N. Rounded to the nearest integer, the answer is B) 30N.

The Horizontal Surface on Which the Objects Slide Is Frictionless