Answer to Question #157514 in Classical Mechanics for Diego

Question

 A boy ties a rope to a 30 kg object, as shown below. He pulls on the rope with a force of 150 N. The rope makes an angle of 20 degrees with the horizontal. The coefficient of friction between the object and surface is .12. Assume that the surface is horizontal and flat.

a.     Draw a free body diagram for the object.

 

 

 

 

b.     Calculate the weight of the object.

 

 

  

 

c.     Calculate the x and y components of the tension in the rope.

 

 

 

d.     Calculate the normal force acting on the object.

 

 

 

 

e.     Calculate the acceleration of the object.

Answer 1

a) Draw the FBD

b) The weight is (green arrow):

$$W=mg=30\cdot9.8=294\text{ N}.$$

с) Calculate the x and y components of the tension in the rope:

$$x:-F\text{cos}20°-f=-ma,\\ N-mg+F\text{ sin}20°=0,\\ f=\mu N.\\\space\\ f=\mu(mg-T\text{ sin}20°)=T\text{cos20°},$$

$$T_x=35.97\text{ cos}20°=33.8\text{ N},\\ T_y=35.97\text{ sin}20°=12.3\text{ N}.$$