A mass of 5 kg is suspended by a rope of length 2 m from the ceiling. A force of 45 N in the horizontal direction is applied at the midpoint R of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium? (Take g = 10 ms-2). Neglect the mass of the rope.

Explanation:

For horizontal equilibrium-

T  

3

​  

=T  

1

​  

sinθ

For vertical equilibrium-

T  

2

​  

=T  

1

​  

cosθ

Taking ratios-

T  

2

​  

T  

3

​  

​  

=tanθ

And for equilibrium of body T  

2

​  

=5kgwt=5×10=50N

⟹tanθ=  

6

5

​  

or θ=tan  

−1

6

5

​

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.