Problems with more than one object Connected Objects

Problems with more than one object, Connected Objects move together : same speed and same Magnitude of acceleration

m. A m. B

FRICTION

Contact force and friction – Figure 5. 10 • We need to re-examine problems we formerly did as “ideal”. • We need to be able to find frictional forces given the mass of the object and the nature of the surfaces in contact with each other. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

The microscopic view of friction – Figure 5. 11 • A surface will always have imperfections, your perception of them depends on the magnification. • The coefficient of friction will reveal how much force is involved. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

DEMONSTRATION Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

Friction changes as forces change – Figure 5. 12 • Forces from static friction increase as force increases while forces from kinetic friction are relatively constant. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

No dependence on surface area – Figure 5. 13 • The normal force determines

Relation Between Normal Force and Maximum Static-Friction Force When the maximum magnitude of the static-friction force can be represented as proportional to the magnitude of the normal force, the two are related by a constant μs called the coefficient of static friction: fs ≤ μsn The equality sign holds only when the applied force parallel to the surface has reached the critical value at which motion is about to start. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

Relation Between Normal Force and kinetic-Friction Force fk =μkn For any given pair of surfaces, the coefficient of kinetic friction is usually less than the coefficient of static friction. As a result, when sliding starts, the friction force usually decreases. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

A person pushes on a stationary 125 N box with 75 N at 30 o below the horizontal, as shown in the figure. The coefficient of static friction between the box and the horizontal floor is 0. 80. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

a) Make a free body diagram of the box b) What is the normal force on the box? c) What is the friction force on the box? d) What is the largest friction force? e) The person now replaces his push with a 75 N pull at 30 o above the horizontal. Find the normal force on the box in this case. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

y n a=0 Fcos 30 o w Fsin 30 o Copyright © 2007 Pearson

Horizontal plane • 3) Force at an angle + friction q A force Fa of 15 N making an angle of 35 o from the horizontal is applied to a block with mass m=6 kg, on a table with friction force Ff opposing the motion of the block of 5. 2 N magnitude. The block was originally at rest when the force was applied. Draw a FBD and find the acceleration of the block and its position after it travels for 5 seconds from the origin Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

FBD There is no motion in the y Direction (the block does not jump !!!) Fy = 0 N Hence: Normal force N = w+Fsin(q) Normal force N y m Ff Fa, y Fa, x q Fa applied force W weight Motion along x: Fa, x – Ff = m ax x ax = (15 N cos (35 o) -5. 2 N)/6 kg Fx = Fcos(q) Fy = Fsin(q) ax = 1. 18 m/s 2 x = xo + voxt + (1/2) axt 2 x = (1/2)(1. 18 m/s 2)(5 s)2 x = 14. 77 m Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

a? n? Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

Forces in fluids – Figure 5. 18 • This topic is fully developed in advanced courses. • Conceptually, observe the drag as objects fall through “thicker” liquids. Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

Elastic forces – Figure 5. 19 • Springs or other elastic material will exert

You find that if you hang a 1. 25 kg weight from a vertical spring, it stretches 3. 75 cm . What is the force constant of this spring in N/m? How much mass should you hang from the spring so it will stretch by 8. 13 cm from its original, unstretched length? Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley

• A surgeon is using material from a donated heart to repair a patient's damaged aorta and needs to know the elastic characteristics of this aortal material. Tests performed on a 16. 0 cm strip of the donated aorta reveal that it stretches 3. 75 cm when a 1. 50 N pull is exerted on it. • What is the force constant of this strip of aortal material? • If the maximum distance it will be able to stretch when it replaces the aorta in the damaged heart is 1. 14 cm what is the greatest force it will be able to exert there? Copyright © 2007 Pearson Education, Inc. publishing as Addison-Wesley