engineering statics · 2019-10-09 · phongpanot phonsanong pages : 1 84th royal jubilee student...

Phongpanot Phonsanong Pages : 1 84th Royal Jubilee Student Scholarship (Civil Engineering) SUT. Former Director-General of Thaiphan Education Centre (TPEC. Administration Officer 9)

Engineering Statics Friction Force and Wedge

REFERENCES: I. Engineering Statics Textbook by R.C. Hibbeler 13th Editions II. Vector Mechanics for Engineers STATICS Textbook by Beer , Johnston , Mazurek and Eisenberg 9th Editions III. Engineering Static worksheet by Assoc Prof. Sittichai Saengatith, Ph.D. IV. Engineering Static worksheet by Assist Prof. Chow Hirantiyakun

Phongpanot Phonsanong Pages : 2 84th Royal Jubilee Student Scholarship (Civil Engineering) SUT. Former Director-General of Thaiphan Education Centre (TPEC. Administration Officer 9)

Wedge (ลิ่ม)

EXAMPLE 1 ............. Friction PART 1

The uniform crate has a mass of 20 kg. If the force P = 80 N is applied as shown, find whether it

remains in equilibrium. The coefficient of static friction s = 0.30

1. Draw FBD of the crate.

2. Use the equations of equilibrium and the equation of

static friction.

EXAMPLE 2

It is observed that the vending machine, weight W, begins to slide of the bed of the dump truck when

the bed inclines = 25o. Compute the coefficient of static friction s between the two surfaces.

1. Draw FBD of the vending machine.

2. Use the equations of equilibrium and the equation of

static friction.

EXAMPLE 3 Determine the maximum and minimum values of weight W1 which may be applied without causing the

weight W (of the black box) to move up and down along the inclined plane. All surfaces have s = 0.25.

2. W is moving upward along the ramp: W1 is

maximum.

2.1 Draw FBD of weight W.

2.2 Use the equations of equilibrium and the

equation of static friction.

1. W is moving downward along the ramp: W1 is

minimum.

2.3 Draw FBD of weight W.



EXAMPLE 4

The uniform 100 N ladder rests against the smooth wall at B and on the rough floor for which s = 0.8. Determine the minimum horizontal force P needed to exert on the ladder in order to cause it to move. ([tip] OR [slide])

1. Draw FBD of the ladder.

2. Use the equations of equilibrium and the


EXAMPLE 5

The three blocks have a weight of WA = 150 N, WB = 250 N and WC = 350 N. If the coefficients of static

friction at the contact surfaces are as shown (s3 = 0.8), find the force P needed to move the block(s).

1. Assume that B is going to slide and C is at rest.

1.1 Draw the FBD of the block A + the block B.



2. Assume that B and C is going to slide simultaneously.

2.1 Draw the FBD of the block A + the block B and C.



EXAMPLE 1 ............. Friction PART 2

Determine the minimum applied force P required to move the wedge A to the right. The spring is compressed a distance of 175 mm. Neglect the weight of the wedge A and the block B. The coefficient of

static friction S between all contacting surface = 0.25. Neglect the friction at the roller.

1. Draw FBD of the wedge A and the block B.

2. Use equations of equilibrium and static friction

and the FBD of the block B.


and the FBD of the wedge A.

Example 2. The 300 N wood box, as shown, rests on the top of the wedge with the contact surface A and the

wedge rests on the 15 degree inclined floor with the contact surface B. All the surfaces has the coefficient of

static friction, 𝜇 = 0.30. Draw the Free Body Diagram (FBD) of the box and the wedge and, then, determine the

minimum force (Pmin), required to move the box downward.

EXAMPLE 3. Determine the smallest force P needed to lift the block, W = 500 N. The coefficient of static

friction s1 = s2 = s3 = 0.25 and = 5o. Neglect the weight of the wedge.

1. Draw FBD of the wedge A and the block B.


and the FBD of the block.


and the FBD of the wedge.

EXAMPLE 4. The wedge is used to level the rigid frame. Compute the minimum force P needed to move the

wedge to the right. The S between the contact surface = 0.25. Neglect the size and weight of the wedge.

1. Draw FBD of the wedge and the frame.


and the FBD of the frame.



EXAMPLE 5. The wedge is used to level the rigid frame. Compute the minimum force P needed to move the

wedge to the left. The S between the contact surface = 0.25. Neglect the size and weight of the wedge.

1. Draw FBD of the wedge and the frame.


and the FBD of the frame..



Problem 1: Determine the minimum horizontal force P required to hold the crate from sliding

down the plane. The crate has a mass of 50 kg and the coefficient of static friction between the

crate and the plane is 𝜇 = 0.25.

Answer: 𝑃 = 140 𝑁

Problem 2: Determine the minimum force P required to push the crate up the plane. The crate

has a mass of 50 kg and the coefficient of static friction between the crate and the plane is 𝜇 =

0.25.


Problem 3: Determine the smallest horizontal force P required to lift the 200-kg crate. The

coefficient of static friction at all contacting surfaces is 𝜇 = 0.3. Neglect the mass of the wedge.

Answer: 𝑃 = 1.98 𝑘𝑁

Problem 4: Determine the smallest horizontal force P required to pull out wedge A.The crate has

a weight of 300 N and the coefficient of static friction at all contacting surfaces is Ps = 0.3. Neglect

the weight of the wedge.

Answer: 𝑃 = 90.7 𝑁

Problem 5: Determine the smallest horizontal force P required to move the wedge to the right.

The coefficient of static friction at all contacting surfaces is 𝜇 = 0.3. Set 𝜃 = 15° and 𝐹 = 400 𝑁.

Neglect the weight of the wedge.


Problem 6: If the uniform concrete block has a mass of 500 kg, determine the smallest horizontal

force P needed to move the wedge to the left. The coefficient of static friction between the

wedge and the concrete and the wedge and the floor is Ps,1 = 0.3 . The coefficient of static friction

between the concrete and floor is Ps,2 = 0.5.

Answer: 𝑃 = 1797.52 𝑁

, I

Problem 7: The coefficient of static friction between the 150-kg crate and the ground is Ps,1 = 0.3,

while the coefficient of static friction between the 80-kg man’s shoes and the ground is Ps,2 = 0.4.

Determine if the man can move the crate.

Answer: He can move the crate because 𝐹 < 𝐹 = 𝜇 , 𝑁

Problem 8: The 3000 kg rear-wheel-drive skid loader has a center of mass at G. Determine the

largest number of crates that can be pushed by the loader if each crate has a mass of 500 kg. The

coefficient of static friction between a crate and the ground is Ps,1 = 0.30, and the coefficient of

static friction between the rear wheels of the loader and the ground is Ps,2 = 0.50. The front

wheels are free to roll. Assume that the engine of the loader is powerful enough to generate a

torque that will cause the rear wheels to slip.

Answer: 𝑛 = 8.82 thus, the largest number of crates that can be pushed by the skid roller is 8

Problem 9: The truck has a mass of 1.25 Mg and a center of mass at G. Determine the greatest

load it can pull if the truck has rear-wheel drive while the front wheels are free to roll. The

coefficient of static friction between the wheels and the ground is 𝜇 = 0.5 , and between the

crate and the ground, it is 𝜇′ = 0.4.

Answer: W = 6.97 kN

Problem 10: The truck has a mass of 1.25 Mg and a center of mass at G. Determine the greatest

load it can pull if the truck has four-wheel drive. The coefficient of static friction between the

wheels and the ground is 𝜇 = 0.5 , and between the crate and the ground, it is 𝜇′ = 0.4.

Answer: W = 15.3 kN

Free Body Diagrams

Problem 1: Problem 2:

Problem 3: Problem 4:

N

Problem 5:

Problem 6:

Problem 7:

Problem 8:

Problem 9:

Problem 10:

engineering statics · 2019-10-09 · phongpanot phonsanong pages : 1 84th royal jubilee student...

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