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

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

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Results: Table 1. Static Friction Coefficient Trial L(m) h(m) θ µ s µ s_average 1 2 3 Insert a picture of your calculations below. (Instructions on how to insert pictures in Word documents are here https://www.youtube.com/watch?v=uL-gEtDkmWY ). Analysis: How does the value of the static friction coefficient you determined compare with what you expected? Procedure B: Kinetic Friction Coefficient 4

1. Tilt the plank (table) at an angle α at which the object can slide down. Choose an angle for which the object does not slide down too fast, so you can have time to measure the travel time. 2. Measure the length L and the height h at the plank (table) and record them in Table 2. 3. Determine the angle α that the plank makes with the horizontal using α = sin -1 (h/L).Record the angle in Table 2. 4. Place the object at the highest end of the inclined plank and let it slide down. 5. Measure the distance x f travelled by the object on the plank (table). The distance travelled by the object is not the length of the plank - it is smaller. Record it in Table 2. 6. Measure the time t it takes the object to travel from the highest end of the inclined plank to its lowest end. 7. Record the time t in Table 2. 8. Calculate the object’s acceleration using equation (3). 9. Record the acceleration in Table 2. 10.Calculate the surface kinetic friction coefficient µ k using equation (2). 11.Record the kinetic friction coefficient. Results: Table 2. Kinetic Friction Coefficient Trial L(m) h(m) α (deg) x f (m) Δt(s) a(m/s 2 ) µ k µ k_average 1 2 3 Insert a picture of your calculations below. (Instructions on how to insert pictures in Word documents are here https://www.youtube.com/watch?v=uL-gEtDkmWY ). Analysis: 5

How does the value of the kinetic friction coefficient you determined compare with what you expected? Take a picture of your experimental setup while you perform the experiment and insert it below. (Instructions on how to insert pictures in Word documents are here https://www.youtube.com/watch?v=uL-gEtDkmWY ). What problems done in lecture and homework involve scenarios identical to the one studied in this lab? 6

Your preview ends here

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