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Jake pulls a couch of mass 23 kg across his apartment. He pulls on the couch at an angle of 32 degrees. with a force of 120 N. The free-body diagram is shown below.


a. What is the x-component of his applied force?


b. What is the y-component of his applied force?


c. Assuming the couch does not leave the ground, what is the normal force acting on the couch?

Jake pulls a couch of mass 23 kg across his apartment He pulls on the couch at an angle of 32 degrees with a force of 120 N The freebody diagram is shown below class=

Respuesta :

a) Simply calculate projection: F.Jake.x=120 cos(32)=101.77 N

b) Likewise: F.Jake.y=120 sin(32)=63.59 N

c) F.N - W + F.Jake.y = 0, so

F.N = W - F.Jake.y = mg - F.Jake.y = 161.81 N

The x-component of his applied force is 101.77 N.

The y-component of his applied force is 63.59 N.

The normal force acting on the couch is 161.81 N.

How to find the x-component of applied force?

  • The x-component of the applied force is the projection of the vector on x-axis.

              So, it will be force applied by jack x sin(32)

                                   =  120 x sin(32)

                                  =  101.77 N

How to find the y-component of applied force?

  • The y-component of the applied force is the projection of the vector on y-axis.

              So, it will be force applied by jack x cos(32)

                                   =  120 x cos(32)

                                   =  63.59 N

How to find the normal force acting on the couch?

  • The resultant force will be 0.
  • Therefore F + (y-component of applied force) - W = 0
  • Here F is normal force acting on the couch and W is force due to gravitation which is mg.

                           So,  F + (y-component of applied force) - W = 0

                               ∴ F = W - (y-component of applied force)

                               ∴ F = mg - (y-component of applied force)

                               ∴ F = 23(9.8) - 63.59

                              ∴ F = 161.81 N

Hence, The x-component of his applied force is 101.77 N.

           The y-component of his applied force is 63.59 N.

            The normal force acting on the couch is 161.81 N.

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