# Topics: Newton’s 2nd Law and Applications

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Topics: Newton’s 2nd Law and Applications
Physics 151 Week 10 Day 2 Topics: Newton’s 2nd Law and Applications Applying Newton’s 2nd Law Apparent Weight Brainstorm: What do we know about friction? Studying Friction

General Force Model Newton 0th Law
Objects are dumb - They have no memory of the past and cannot predict the future. Objects only know what is acting directly on them right now Newton's 1st Law An object that is at rest will remain at rest and an object that is moving will continue to move in a straight line with constant speed, if and only if the sum of the forces acting on that object is zero. Newton's 3rd Law Recall that a force is an interaction between two objects. If object A exerts a force on object B then object B exerts a force on object that is in the opposite direction, equal in magnitude, and of the same type. Visualizations: Force Diagrams System Schema

Constant Force Model Newton's 2nd Law
acceleration of an object = sum of forces acting on that object / the mass of the object Remainder of week: Friction Model Apparent Weight Slide 4-19

Another look at the double-ended fan-cart
Slide 5-27

Example Problem A 100 kg block with a weight of 980 N hangs on a rope. Which Force is larger, FT, rope => block or Fg, Earth => block? the block is stationary. it’s moving upward at a steady speed of 5 m/s. it’s accelerating upward at 5 m/s2. Slide 5-15

Example Problem A 100 kg block with a weight of 980 N hangs on a rope. Find the tension in the rope if the block is stationary. it’s moving upward at a steady speed of 5 m/s. it’s accelerating upward at 5 m/s2. Slide 5-15

Example Problem A sled with a mass of 20 kg slides along frictionless ice at 4.5 m/s. It then crosses a rough patch of snow which exerts a friction force of 12 N. How far does it slide on the snow before coming to rest? Slide 5-21

Example Problem A 75 kg skier starts down a 50-m-high, 10° slope on frictionless skis. What is his speed at the bottom? Slide 5-27

Scales and Elevators (Apparent Weight)
Consider a person with a mass of 60 kg is in an elevator standing on a scale. The elevator is accelerating upward. Draw a system schema and 2 force diagrams: One for the person and one for the scale What does the scale read? Use Newton’s 2nd law to determine what the scale reads (This is apparent weight) Slide 4-19

Apparent Weight Slide 5-24

Scales and Elevators (Apparent Weight)
Suppose a person with a mass of 60 kg is in an elevator standing on a scale. Use the system schema and force diagrams of the scale and the person to determine what the scale would read for the following situations: A. If the elevator is descending at 4.9 m/s. B. If the elevator has a downward acceleration of 4.9 m/s/s. C. If the elevator has an upward acceleration of 4.9 m/s/s. Slide 4-19

Example Problem A 50 kg student gets in a 1000 kg elevator at rest. As the elevator begins to move, she has an apparent weight of 600 N for the first 3 s. How far has the elevator moved, and in which direction, at the end of 3 s? Slide 5-25

Clicker Question The apparent weight of an object is
the pull of gravity on the object. the object’s mass times the acceleration of gravity. the magnitude of the contact force that supports the object. the pull of gravity on an object that is accelerating upward. Answer: C Slide 5-7

Answer The apparent weight of an object is
the pull of gravity on the object. the object’s mass times the acceleration of gravity. the magnitude of the contact force that supports the object. the pull of gravity on an object that is accelerating upward. Answer: C Slide 5-8

Friction Brainstorm One person in each team takes out a sheet of paper and records their group brainstorming everything they know about friction.

Example Problem Burglars are trying to haul a 1000 kg safe up a frictionless ramp to their getaway truck. The ramp is tilted at angle θ. What is the tension in the rope if the safe is at rest? If the safe is moving up the ramp at a steady 1 m/s? If the safe is accelerating up the ramp at 1 m/s2? Do these answers have the expected behavior in the limit θ → 0° and θ → 90°? Slide 5-28

Example Problem Macie pulls a 40 kg rolling trunk by a strap angled at 30° from the horizontal. She pulls with a force of 40 N, and there is a 30 N rolling friction force acting on trunk. What is the trunk’s acceleration? Slide 5-22

Demonstrations: What do we know about Friction Force?
2 - Increases with more contact surface - Not dependent on surface area, but surface type Does our model of friction depend on area? Does real-world friction depend on area?

Parking on a Hill If you park on a hill with a 10 degree slope with the car held by the parking brake, what is the magnitude of the frictional force that holds your car in place? The coefficient of static friction between your car's wheels and the road when wet is What is the largest angle slope on which you can park your car in the rain so that it will not slide down the hill? The coefficient of kinetic friction between your wheels and the wet road surface is If someone gave your your car a push on the wet hill and it started sliding down, what would its acceleration be? Slide 4-19

Penguin in a box A loaded penguin in a box, together weighing 60 N, rests on a plane inclined at 20° to the horizontal. Between the box and the plane, the coefficient of static friction is 0.26 and the coefficient of kinetic friction is 0.15. What is the minimum magnitude of the applied force F, parallel to the plane, that will prevent the sled from slipping down the plane? What is the minimum magnitude of the applied force F that will start the sled moving up the plane? What value of the applied force F is required to move the block up the plane at constant velocity? Hint: Draw a system schema and then draw a separate force diagram for each part of the problem

Haul the Crate A 10 kg wooden crate is placed on wood slats in the back of a pick-up truck with no tail gate. How fast can the truck accelerate before the crate falls off? Assume the coefficient for static friction for the crate on the wood slats is 0.40 and the coefficient for kinetic friction is 0.20.

Brainstorm: What do we know about Friction Force?
Seems to relate to pushing force (Drag Force?) - Increases with more contact surface - Not dependent on surface area, but surface type Car needs friction for acceleration including steering Can determine acceleration along with other forces 2 types static and kinetic, once object starts moving crosses from Ffs to Ffk / also rotational/rolling Friction is smallest friction Caused by electron repulsion between two objects - Friction opposes (in opposite direction of) applied force - Direction of Friction force is Opposite of direction of motion / acceleration - Parallel to motion / Resists force of acceleration Friction Force is a contact force that acts on an object by its surface Converts Kinetic Energy to Thermal Energy Friction Force depends on what is in contact (involves a coefficient ) Friction is resistance between 2 surfaces in contact / resists change Friction does not depend on mass / related to weight It slows things down and makes them stop (can be small/negligible) Can occur doing motion or without motion It acts two ways It usually accompanies a normal force / perpendicular to normal force It is in the negative y direction, parallel to the surface of an object Ffs > Ffk - initially starting object moving is harder than keeping it moving

Static & Kinetic Friction Describe what is happening to the forces on the box and the effect of the forces on the motion of the box from the pictures. Slide 4-19

Static & Kinetic Friction - Part III
Below is graph of the friction force exerted by the table on the box.   Label times a-f that match the free-body diagrams in the previous problem. If the mass of the box is 3.0 kg, the maximum Ffs is 10 N, and Ffk has an average of 6.0 N, find the coefficients of static and kinetic friction. Slide 4-19

Demonstrations: What do we know about Friction Force?
2 - Increases with more contact surface - Not dependent on surface area, but surface type Does our model of friction depend on area? Does real friction depend on area?

Demonstration: What do we know about Friction Force?
7 - Friction opposes (in opposite direction of) applied force - Direction of Friction force is Opposite of direction of motion / acceleration - Parallel to motion / Resists force of acceleration Does friction always oppose motion?

Brainstorm: What do we know about Friction Force?
18. Ffs > Ffk - initially starting object moving is harder than keeping it moving

Coefficients of Friction
What can you deduce/generalize about friction forces from this table? Describe 3-4 real world situations that can be explained by this table Slide 4-19

Clicker Question The coefficient of static friction is
smaller than the coefficient of kinetic friction. equal to the coefficient of kinetic friction. larger than the coefficient of kinetic friction. equal to or larger than the coefficient of kinetic friction not discussed in this chapter. Answer: C Slide 5-9

Answer The coefficient of static friction is
smaller than the coefficient of kinetic friction. equal to the coefficient of kinetic friction. larger than the coefficient of kinetic friction. equal to or larger than the coefficient of kinetic friction not discussed in this chapter. Answer: C Slide 5-10