A cable with a tension of 45 N is used to suspend a 5 kg mass M against a wall. What is the magnitude and direction of the force of friction between the mass and the wall?

Question

A cable with a tension of 45 N is used to suspend a 5 kg mass M against a wall.  What is the magnitude and direction of the force of friction between the mass and the wall?

Quizplus · Accepted Answer

11ecba2d_130e_bb9d_a3bf_03764543d973_MD0008_00 Any object may be acted on by multiple translational forces of different origin, magnitude, and direction. For example, an object located in two-dimensional space will accelerate when the sum of all forces acting along one or both axes of the xy-coordinate system does not equal zero. Because forces acting along the same axis can be either antagonistic or cooperative, free-body diagrams can be used to assess the balance of forces along each axis provided that the vector components of each force are known: 11ecba2d_130e_e2ae_a3bf_25411bb3d705_MD0008_00 11ecba2d_130e_e2af_a3bf_891f1dcfef9e_MD0008_00 When the sum of all forces acting on a mass along each axis of the xy-coordinate system is equal to zero, the object is said to be in equilibrium such that no acceleration occurs: 11ecba2d_130e_e2b0_a3bf_415cee99d458_MD0008_00 11ecba2d_130e_e2b1_a3bf_f9d7f6f5f489_MD0008_00 In contrast to an equilibrium in which an object is moving, static equilibrium results when the balance of forces acting on an object maintains the absence of motion by that object. In the prompt, a 5 kg mass is suspended in static equilibrium by a cable with a tension of 45 N. Isolating only the vertical (y-axis) forces, the magnitude of the gravitational force acting on the object can be determined by the simple equation for weight: 11ecba2d_130e_e2b2_a3bf_495e406f8342_MD0008_00 Because this downward (−y) gravitational force acting on the mass is greater than the 45 N tension force pulling the block upward (+y), it can be concluded that the frictional force acting on the mass must act in an opposing, upward (+y) direction to maintain the static equilibrium. Using the equation for static equilibrium, the magnitude of the frictional force (F_f) between the mass and the wall can be calculated: 11ecba2d_130f_09c3_a3bf_8f04903e6d82_MD0008_00 11ecba2d_130f_09c4_a3bf_590d1fbe07ed_MD0008_00 11ecba2d_130f_09c5_a3bf_4791b680f06e_MD0008_00 11ecba2d_130f_09c6_a3bf_81a491d7b8e2_MD0008_00 N and oriented in an upward (+y) direction (Choice A). Educational objective: Static equilibrium occurs when the sum of all forces acting on a motionless object is equal to zero. Free-body diagrams are used to illustrate the directional components of translational forces.

A Cable with a Tension of 45 N Is Used