Announcements THERE WILL BE NO CLASS THIS FRIDAY, MARCH 5 (We are 1 full lecture ahead of the syllabus, so we will still have review/problem solving on March 7 and 9). There will still be a WebAssign due this Friday, the last before the midterm. Instead of a written homework, I will create a mock exam within WebAssign that will not count toward your grade, and which will contain tutorials, worked solutions, etc. A practice midterm 2 with answers (not worked solutions), as well as a selection of practice WebAssign questions with answers, can be found at http://community.wvu.edu/ ~miholcomb/phys101.html under Additional Materials. Midterm 2 will be on March 9, 5 PM - 7 PM in G09 (room change). Midterm 3 will be on April 13, 5 PM - 7 PM in G09 (day and room change). The makeup exams will both be the Friday after the main exams (March 11 and April 15, respectively), 3:30 PM - 5:30 PM in White G04
Practice question A cable attached to a car holds the car at rest on the frictionless ramp (angle α). The ramp exerts a normal force on the car. How does the magnitude n of the normal force compare to the weight w of the car? A. n = w B. n > w C. n < w D. not enough information given to decide
Inclines 1. The gravitational force: Direction: Straight down - perpendicular to the surface of the earth, not the inclined surface! Fg must be split up into a component parallel to the inclined surface and perpendicular to it: FII = -mg sin(θ); F = -mg cos(θ) FII accelerates the object downwards. 2. The normal force: Direction: Opposite to F (compensating it) 3. A force in the opposite direction of FII, e.g. friction or a tension force (rope)
Example problem
Before the crate moves
After the crate starts moving
Practice question A block moves to the right in the positive x-direction while under the influence of a force. Which of the following is the correct order of the amount of work done by the force from most positive to most negative? A. d, c, a, b B. c, a, b, d, C. c, a, d, b D. b, a, c, d
Work and kinetic energy The work, W, done by a constant force on an object during a linear displacement along the x- axis is: Positive/negative work means that the force and the displacement are in the same/opposite directions. There are 2 types of forces: 1. Conservative: Work does not depend on path 2. Non-conservative: Work depends on path Work-Energy Theorem: Here, 1/2mv 2 is the kinetic energy. Energy is never lost, but can only be transformed to other kinds of energy.
Example problem An Inuit pulls a sled loaded with salmon. The total mass of the sled and the salmon is 50 kg. The Inuit exerts a force of magnitude 120 N on the sled by pulling on the rope. A. How much work does he do on the sled, if the rope is horizontal to the ground and he pulls the sled 5 m? B. How much work does he do on the sled if θ = 30 and he pulls the sled the same distance? C. At a coordinate position of 12.4 m, the Inuit lets up on the applied force. A friction force of 45 N between the ice and the sled brings the sled to rest at 18.2 m. How much work does friction do on the sled?
Potential Energy Every conservative force can be associated with a potential energy, i.e. an energy that allows the corresponding object to potentially do work. One example of such a conservative force is gravitation. The gravitational potential energy is: Another important conservative force is the force that springs exert on objects according to Hooke s law: The spring potential energy is:
Example problem: Gravitational potential energy A book of mass 3 kg is lifted from a height of 2 m above the floor to a height of 3 m above the floor. What is the corresponding increase of the book s gravitational potential energy?
Conservation of energy If non-conservative forces can be neglected, the sum of potential and kinetic energy will be conserved. Typical problems that can be solved by energy conservation: Rollercoasters, Pendulums, Jumping.
Example problem: Conservation of energy A ball is attached to a pendulum. The ball is initially held at rest at a height of 30 cm above the floor. Then, the pendulum is allowed to oscillate. Neglect friction. What is the ball s velocity at the lowest point of its trajectory?
Power Power is the rate at which energy is transformed from one type to another: Average power: Power is a scalar quantity. Unit: Alternative expression for power: if F is parallel to Δx.
Example problem: Power A bicyclist coasts down a 7.0 o hill at a steady speed of 5.0 m/s. Assuming a total mass of 75 kg (bicycle plus rider). What must be the cyclist s power output to climb the same hill at the same speed?
Momentum and Impulse Definition of linear momentum: Unit: kg m/s Momentum is a vector quantity. It points into the same direction as the object s velocity. Relation between momentum and kinetic energy: Relation between force and impulse: Definition of impulse: Impulse corresponds to a change of momentum during a time interval Δt. F m vi m vf
Example problem: Car crash In a crash test, a car of mass 1500 kg collides with a wall and rebounds as shown in the figure. The initial and final velocities of the car are vi = -15 m/s and vf = 2.6 m/s, respectively. If the collision lasts for 0.15 s, find A. the impulse delivered to the car due to the collision. B. the size and direction of the average force exerted on the car.
Collisions There are three types of collision processes: Inelastic, elastic, and superelastic collisions Inelastic collisions: Momentum is conserved, energy is not conserved (lost). If the colliding objects stick to each other, the collision is perfectly inelastic: Elastic collisions: Momentum and energy are conserved. Superelastic collisions: Momentum is conserved, energy is not conserved (gained)
Example problem: Elastic collisions A 25 g object moving to the right at 0.2 m/s collides elastically with a 10 g object moving in the same direction at 0.15 m/s. Find the velocity of each object after the collision. Typical situation: 2 unknowns and 2 equations Recipe: Solve one equation for one unknown and substitute the result into the other equation.