lab4

.docx

School

Montgomery College *

*We aren’t endorsed by this school

Course

203

Subject

Mechanical Engineering

Date

Dec 6, 2023

Type

docx

Pages

Uploaded by CaptainMusicCoyote13 on coursehero.com

Name: Friction Objective  Apply Newton’s 2 nd Law to measure the coefficient of static and kinetic friction. Equipment  a small object (pencil, toothpaste container, a small cream container, etc.)  a table(or a wood/plastic plank) longer than 1m, that you can tilt to create an incline  books to support the inclined table (plank)  ruler (or measuring tape)  cell phone timer Theoretical Setup Static Friction Coefficient When an object in contact with a surface just starts to move, has to overcome the static friction force. Consider an object on a horizontal surface and imagine that you incline the surface until the object just starts to slide down. At that instant, the static friction force opposes the motion of the object and the object can be considered in equilibrium. The free body diagram for this object is illustrated in Fig.1. Figure 1. Object in Equilibrium 1 y N x f s m g sin   m g cos  m g

When we apply Newton’s 2 nd Law F net = m a for this object in equilibrium, we write it along each axis: F netx = 0 F nety = 0 Based on the free body diagram, the above equations become: mgsin   f s = 0 N - mgcos  = 0 Replacing f s =µ s N, we obtain: mgsin   µ s N = 0 N - mgcos  = 0 By eliminating the normal force N between the two equations and solving for the static friction coefficient µ s , we obtain: µ s = tan  (1) Kinetic Friction Coefficient When an object slides down on a tilted surface, is acted upon by the kinetic friction force. The free body diagram for such an object is illustrated in Fig.2. Figure 2. Object Sliding Down When we apply Newton’s 2 nd Law F net = m a for this object, we write it along each axis: 2 a y N x f k m g sin  α m g cos  m g

F netx = ma F nety = 0 From the free body diagram, it becomes: mgsin α  f k = ma N - mgcos α = 0 Replacing f k =µ k N, we obtain: mgsin α  µ k N = ma N - mgcos α = 0 By eliminating the normal force N between the two equations and solving for the kinetic friction coefficient µ k , we obtain: µ k = (gsin α  a  (gcos α  (2) Consider an object that slides down on an incline. Staring from rest, the object travels distance L in the time interval Δt. From the kinematic equation x f = x i + v i Δt +1/2 a(Δt) 2 , we solve for the acceleration a: a=2x f /( Δ t) 2 (3) Knowing the acceleration from equation (3), we can use equation (2) to compute the kinetic friction coefficient between the incline and the object. Experimental Procedures Procedure A: Static Friction Coefficient 1. Place your object on the middle of the plank (table). 2. Slowly raise one end of the plank until the object just begins to slide. 3. Find the angle of inclination  . When tilting the plank (table), a right triangle is formed. Measure the length (L) and the height (h) of the plank. Calculate the angle  that the plank (table) makes with the horizontal using  = sin -1 (h/L). 4. Record the angle in Table 1. 5. Calculate the static friction coefficient µ s using equation (1). 6. Record the static friction coefficient in Table 1. 7. Repeat steps 2-4 three times. 8. Calculate the average static friction coefficient. Record the average static friction coefficient in Table 1. 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version