EME 231 Engineering Statics: Fall 2007

EGR 231 Engineering Statics: Fall 2014Lecture 31: Tipping ForceToday:

Analysis of Tipping vs. Friction

Homework 31:

Problem 8.19

A 60 kg cabinet is mounted on caster which can be locked to prevent their rotation. The coefficient of static friction is 0.35. If h = 600 mm, determine the magnitude of the force required to move the cabinet to the right

a) if all casters are locked b) if the casters at B are locked and the casters at A are free to rotate, c) if the casters at A are locked and the casters at B are free to rotate.

Problem 8.21

A packing crate of mass 40 kg must be moved

to the left along the floor without tipping.

Knowing that the coefficient of static friction

between the crate and the floor is 0.35, determine

a) the largest allowable value of .

b) the corresponding magnitude of the force P.

Problem 8:28A cord is attached to and partially wound around a

cylinder of weight W and radius r which rests on

an incline as shown. Knowing that = 30o. find

a) the tension in the cord,

b) the smallest value of the coefficient of static

friction between the cylinder and the incline for

which equilibrium is maintained.

Friction: Sliding vs. Tipping

When dealing with bodies that are relatively tall or with surfaces that have high coefficients of friction, it is possible that a body will respond to a force by tipping instead of sliding.

To test for sliding: Determine what force is needed to exceed the point of impending motion:

To test for tipping: Determine what force is needed to exceed the restoring moment about the most extreme point of contact.

Problem 1:

What force is needed to make the container slide?

What force is needed to make the container tip?

Which one occurs first?

Check sliding:

Friction Eq:

For Equilibrium:

so combining:

force required to slide:

Check tipping: For Equilibrium

force required to tip.Since the body will slip instead of tip.Problem 2:

Determine the minimum force P needed to push the tube E up the incline. The tube E has a mass of 75 kg and the roller D has a mass of 100 kg. The force acts parallel to the plane, and the coefficient of static friction at the contacting surfaces are A = 0.3, B = 0.25, and C = 0.4. Each cylinder has a radius of 150 mm.Qualitative Pre-analysis:If the solid cylinder rolls up the plane

without sliding at C, then the hollow cylinder

must either slip at A or B.

It would also be possible for the hollow

cylinder to not slip at A or B, if the solid

cylinder slips at C.

What this means is that whichever point of

A, B, or C exceeds the point of impending moment for the lowest value of P will be the spot where the cylinders slip. This is the force you wish to find.

Possible Solution 1:Assume slippage of the hollow cylinder occurs at point B:

Drum: For Equilibrium

(

Hollow Cylinder:

(

Friction Equation (only applies at surface which slips)

Next solve the 7 equations for the 7 unknowns:

First reduce the FfA, FfB, and FfC, terms:

(

(

(

Next reduce NA and NC:

Now solve the first equation for P:

therefore for B =0.25, =30o, WE = 736N and WD = 981 N

Possible Solution 2: Assume slippage between cylinders occur at point A.

The FBDs are the same, so the Equilibrium equation are the same:

For slip at A, the Friction Equation applies only at A.

Once again, reduce these equations to find P.Using

gives

(

(

(

so

and then P can be found as

Possible Solution 3: Assume slippage of the disk occurs at C.

The FBDs are the same, so the Equilibrium

equation are the same:

For slip at C, the Friction Equation applies only at C.

Once again, reduce these equations to find P.

Using

gives

(

(

(

so

and then P can be found as

so

Since the minimum force occurs when B slides, the force needed is 1071 N. Extra Problems:

Problem Ex1

A 6.5 m ladder AB of mass 10 kg leans against a wall as shown. Assuming that the coefficient of static friction s is the same at both surfaces of contact, determine the smallest value of s for which equilibrium can be maintained.

Problem Ex2Blocks A, B, and C having the weights shown are at rest on an incline. Denoting by s the coefficient of static friction between all surfaces of contact, determine the smallest value of s for which equilibrium is maintained.

slide

tip

P

P

s = 0.3

P

5 ft

3 ft

G

A

2.5 ft

W=100 lbf

P

W

N

Ff

P

W

N

Ff

1.5

ft

2.5 ft

30o

P

A

E

C

D

B

FfB

NB

WE

FfA

NA

WD

P

FfC

NC

FfA

NA

FfB

NB

WE

FfA

NA

WD

P

FfC

NC

FfA

NA

FfB

NB

WE

FfA

NA

WD

P

FfC

NC

FfA

NA

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