Physics 1D03 - Lecture 22

Energy Examples

Serway and Jewett 8.1 – 8.3

Physics 1D03 - Lecture 22

Conservative Forces

A force is called “conservative” if the work done (in going from some point A to B) is the same for all paths from A to B.

An equivalent definition:

For a conservative force, the work done on any closed path is zero. Later you’ll see this written as:

Total work is zero.

path 1

path 2A

B

W1 = W2

Physics 1D03 - Lecture 22

If only conservative forces do work, potential energy is converted into kinetic energy or vice versa, leaving the total constant. Define the mechanical energy E as the sum of kinetic and potential energy:

E K + U = K + Ug + Us + ...

Conservative forces only: W UWork-energy theorem: W K

So: KU 0

Conservation of mechanical energy

Physics 1D03 - Lecture 22

Concept Quiz

You drop two rocks from top of a building. One has mass m and the other mass 2m. When they hit the ground

A) they have the same speed and same kinetic energy

B) they have the same speed but the first rock has more kinetic energy

C) they have the same speed but the second rock has more kinetic energy

D) the second rock has a higher speed and more kinetic energy

Physics 1D03 - Lecture 22

Concept Quiz

A particle is acted upon by only two forces, one conservative and one non conservative, as it moves from point A to point B. The kinetic energies of the particle at points A and B are equal if:

A) The sum of the works done by the two forces is zero.B) The work done by the conservative force is equal to the work done by the non conservative force.C) The work done by the conservative force is zero.D) The work done by the non conservative force is zero.

Physics 1D03 - Lecture 22

Concept Quiz

If the total mechanical energy of a particle decreases, then it is necessarily true that:

A) the kinetic energy decreasesB) the work done by the conservative forces is negativeC) the work done by non-conservative forces is negativeD) the net work done by all forces is negative

Physics 1D03 - Lecture 22

Example 1

A 10kg block on a horizontal surface is attached to a spring with k=0.8 kN/m. The block is initially at rest at it’s equilibrium position when a constant force P=80 N acts parallel to the surface and is applied to the block. What is the speed of the block when it has moved 13 cm from its equilibrium position?

Physics 1D03 - Lecture 22

Example 2

A 6 kg block initially at rest is pulled to the right along a horizontal surface by a constant force of P=12 N. Find the speed of the block after it has moved d=3 m if the surface has a coefficient of kinetic friction of 0.15.

Physics 1D03 - Lecture 22

Example 3

A block initially at rest is pulled to the right along a horizontal surface that has μk = 0.15 by a constant force F, which acts at an angle of θ above the horizontal. Find the angle that will achieve the maximum possible speed after the block has been pulled a distance d.

Physics 1D03 - Lecture 22

Solution

Physics 1D03 - Lecture 22

Example 4

A 2.0-kg block situated on a frictionless incline (angle 37o to the horizontal) is connected to a light spring (k = 100 N/m), as shown. The block is released from rest when the spring is unstretched. The pulley is frictionless and has negligible mass. What is the speed of the block when it has moved 0.20 m down the plane?

Physics 1D03 - Lecture 22

Solution