A 10-kg block is suspended in air by a single string that passes through a pulley and is attached on the other side to a 35-kg block that is on the verge of sliding on the ground. What is the coefficient of static friction between the larger block and the ground? (Note: The magnitude of the vertical force the small block exerts on the large block is 87 N.)

Question

A 10-kg block is suspended in air by a single string that passes through a pulley and is attached on the other side to a 35-kg block that is on the verge of sliding on the ground.  What is the coefficient of static friction between the larger block and the ground?  (Note: The magnitude of the vertical force the small block exerts on the large block is 87 N.)

Quizplus · Accepted Answer

11ecba2d_1330_7490_a3bf_d15742fbc1bf_MD0008_00 Attractive intermolecular forces between the atoms of two surfaces contribute to frictional forces that oppose motion along the interface between two objects that are in direct contact with one another. In a static equilibrium (ie, motionless, with a balance of forces), a frictional force that resists the initiation of motion is called static friction. Static friction is oriented parallel to the contacting surfaces and arises antagonistically in response to a force that attempts to move an object within the system. The maximum magnitude of static friction (F_s) between two opposing surfaces is equal to the product of the normal force (F_N) and the coefficient of static friction (μ_s), a unitless coefficient related to the characteristics of the contacting surfaces: 11ecba2d_1330_9ba1_a3bf_13f3053c7ca0_MD0008_00 If the force applied to an object does not exceed F_s, the object will not move. Conversely, if F_s is exceeded, the object will accelerate, and static friction will become kinetic friction. In this question, a 35-kg block located on the ground remains motionless despite an applied force from a 10-kg block suspended by a fixed pulley. The pulley redirects the weight of the smaller block (W_SB) into two component forces oriented along the x- and y-axes. The magnitude of the horizontal force (F_x) applied to the larger block is: 11ecba58_d7ab_c661_99fe_c1e3a6e392a1_MD0008_11 And the vertical force (F_y) is: 11ecba58_f39e_29d2_99fe_119d87ca560d_MD0008_11 Because the block is still in static equilibrium, F_s must be equal to F_x: 11ecba2d_1330_c2b7_a3bf_8f700e680ad2_MD0008_00 Furthermore, F_N between two terrestrial objects is typically proportional to the weight of the object located above the other. Consequently, F_N between the large block and the ground is equal to the weight of the larger block (W_LB) minus the vertical (y-axis) force (F_y) acting to lift the block: 11ecba2d_1330_c2b8_a3bf_abeec045fd5c_MD0008_00 11ecba2d_1330_c2b9_a3bf_93b5d56d21f3_MD0008_00 11ecba2d_1330_c2ba_a3bf_d9825a737487_MD0008_00 11ecba2d_1330_c2bb_a3bf_e7fce7354739_MD0008_00 Therefore, μ_s between the large block and the ground is 0.19 (Choice C). Educational objective: Static friction is an antagonistic force acting within a static equilibrium to prevent motion along the interface between two objects in direct contact. The maximum magnitude of static friction is the product of the normal force and the coefficient of static friction.

A 10-Kg Block Is Suspended in Air by a Single