Chapter 5: Applications of Newton s Laws

Transcription

1 Chapter 5: Applications of Newton s Laws Brent Royuk Phys-111 Concordia University Friction Definition: a that opposes motion Three types Static Contact Kinetic Sliding Rolling Friction depends on two things The load Nature of the two surfaces Smooth vs. scratchy Real friction: Van der Waal s Forces Cold welding of metals Consider: What would you do if you were on a completely frictionless surface? 2 Friction 3 1

2 Friction Load 4 Kinetic Friction f k = µ k N What is µ k? Coefficients: Table 5.1, p. 165 and next slide Kinetic Friction is: Proportional to N Independent of the relative speed of the surfaces Independent of the area of contact of the surfaces 5 6 2

3 Kinetic Friction Examples Someone at the other end of the table asks you to pass the salt. Feeling quite dashing, you slide the 50.0-g salt shaker in their direction, giving it an initial speed of 1.15 m/s. If the shaker comes to rest with a constant acceleration in m, what is µ k? Suppose you then lift up the table and incline it at an angle of 22 o. Then you give the shaker a push. What acceleration does the shaker experience as it slides down the table? 7 Static Friction What is the nature of friction between surfaces that are at rest with respect to each other? What does it mean that µ s > µ k? 8 Static Friction The static friction laws: 0 f s f s max f s max = µ s N The Crate Problem A worker wishes to use a rope to pull a 40.0-kg crate across a floor. What force is necessary to get it moving if µ s = 0.650? If he keeps pulling with that force and µ k = 0.450, what will the acceleration of the crate be? Rework the problem with the worker pulling at a 30.0 o angle. Place a penny on a board. Lift the board until the penny just starts to slide and measure the angle θ. What is µ s? 9 3

4 Strings and Springs String tension Strings can t push, can only pull Heavy vs. ideal Ideal pulleys merely change direction Springs follow Hooke s Law F = -kx The spring constant, k Units Meaning Examples A 10 kg weight and a 5 kg weight are hung from a string, one above another. An upward force of 170 N is applied. What are the string tensions and the acceleration of the block? Standard Trick #1 Two blocks of mass m 1 = 2.5 kg and m 2 = 3.5 kg are side-by-side on a frictionless table and connected by a string. A horizontal force of 12.0 N is applied to the block on the left. Find the acceleration of the blocks and the tension of the connecting string. 12 Examples Find T in terms of m, g and θ. F θ T m 14 4

5 Examples Find the acceleration of Atwood s Machine in terms of its masses m 1 and m 2. Find the string tension. Standard Trick #2 Given m 1 on an inclined plane at 32 o, m 2 hanging over a pulley at the top and pulling up the plane. m 1 = 4.0 kg; m 2 = 3.5 kg, µ k = The box is moving up the plane. What is the acceleration? Desk Problem: At a 30 o angle, a box accelerates down an inclined plane at a rate of 0.85 m/s 2.. Find µ k. 15 The Drag Force An object moving through a fluid experiences a drag force. cannon ball sinking in water, car on highway, baseball, parachutist, dust, coffee filters F drag α v 2 At terminal speed, F drag = mg Equation: F drag = 1 Cρ Av2 2 v t = 2mg CρA ρ is the density of the fluid (1.2 kg/m 3 for air), A is cross-sectional area, C is the shape coefficient, generally ranging from (next slide)

6 Some Approximate Terminal Speeds Object Speed (m/s) cannonball lb shot 145 high caliber bullet 100 sky diver baseball 42 tennis ball 31 basketball 20 mouse 13 ping-pong ball 9 penny 9 raindrop 7 parachutist 5 snowflake 1 sheet of paper (flat) 0.5 fluffy feather 0.4 You can drop a mouse down a thousand-yard mine shaft and, on arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes. -J.B.S. Haldane, British geneticist, Elevator Dynamics If you stand on a scale in an accelerating elevator, what does the scale read (W )? Scenarios: at rest or constant speed: W = W = mg a = g/2 up a = g/2 down cable breaks a = 2g up a = 2g down So could you jump at the last second in a freefalling elevator in order to survive? 19 6