The horizontal surface on which the objects slide is frictionless.If M = 2.0 kg,the tension in string 1 is 12 N.Determine F.
A)25 N
B)20 N
C)30 N
D)35 N
E)40 N

Question

The horizontal surface on which the objects slide is frictionless.If M = 2.0 kg,the tension in string 1 is 12 N.Determine F. 
A)25 N 
B)20 N 
C)30 N 
D)35 N 
E)40 N

Quizplus · Accepted Answer

Since the tension in string 1 is given as 12 N, it means that tension in string 2 is also 12 N (since the pulley is ideal and massless). Using Newton's second law, we can set up equations for the forces acting on the masses:
Mg - T1 = Ma  (for mass M)
T2 - mg = Ma   (for mass m)
Solving for acceleration in each equation:
a = (Mg - T1)/M
a = (T2 - mg)/m
Since the surface is frictionless, there is no horizontal force acting on the system. This means that the tension force T2 must be equal to F, the force pulling mass m horizontally. 
Replacing T2 with F in the second equation above:
a = (F - mg)/m
Since both accelerations must be equal (due to the pulley being massless and not causing any net acceleration), we can set the two expressions for acceleration equal to each other and solve for F:
(Mg - T1)/M = (F - mg)/m
Plugging in the given values, we get:
(2*9.81 - 12)/2 = (F - 2*9.81)/1
Simplifying, we get:
F = 20 N (rounded to the nearest whole number)

The Horizontal Surface on Which the Objects Slide Is Frictionless