Phy 2053 Announcements Exam 1 Feb 17 Wednesday, 8:20 – 10:10 pm Please get there at least 10 minutes early Covers Chapters 1 - 5 (includes Lecture on Feb 11 Th) Room assignments If your last name begins with A through O, you should go to Carleton 100 If your last name begins with P through Z, you should go to McCarty C 100 You will be allowed one handwritten formula sheet (both sides) Sample exam from last year posted on website. Previous exams & solutions available at Target copy. Review: Energy and Work Work done by a force F on an object: W ≡ (F cos θ)∆x Can Be Positive or Negative Kinetic Energy: 1 2 KE = mv 2 Gravitational potential Energy: PE = mgy Conservation of Mechanical Energy In any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant. Ei = E f KEi + PEi = KE f + PE f Problem 5.46 (modified) A child of mass m starts from rest and slides without friction from a height h along a curved waterslide. She is launched from a height h/5 into the pool. Find the max height y after she leaves the waterslide. Force is a vector: When applying Newton’s law, we write the x and y components separately: ∑F x = ma x ∑F y = ma y Energy is a scalar: do NOT write energy conservation separately in x and y components KEi + PEi = KE f + PE f Non-conservative forces and mechanical energy If nonconservative forces are present, then the full Work-Energy Theorem must be used instead of the equation for Conservation of Energy Wnc = (KEf- KEi) + (PEf-PEi) Wnc = (KEf+PEf) - (KEi+PEi) Total final mechanical energy Total initial mechanical energy Example: work-energy theorem The pendulum (mass 2 kg, length 4 m) is released from rest, at an angle of 30 degrees from the vertical. When the pendulum comes back, it only reached 28 degrees to the vertical. Find the work done by nonconservative forces (friction and air resistance) on the mass. Wnc = (KEf+PEf) - (KEi+PEi) Spring Force Hooke’s Law gives the force F=-kx F is the restoring force F is in the opposite direction of x k is spring constant k is larger for a stiffer spring x = 0 is the equilibrium position F Slope = -k x Work done by a Spring only valid for a W ≡ (F cos θ)∆x constant force F In a spring F varies linearly with x: F = - k x To calculate work done by the spring, we need to use the average force: Faverage F0 + F1 0 + (−kx) kx = = =− 2 2 2 1 2 kx Work done by the spring = Ws = Faverage x = − ( x) = − kx 2 2 Potential Energy in a Spring 1 2 PE s = kx 2 Spring + Gravity Wnc = (KEf – KEi) + (PEgf – PEgi) + (PEsf – PEsi) PEg is the gravitational potential energy PEs is the elastic potential energy associated with a spring PE will now be used to denote the total potential energy of the system Conservation of Energy: Spring + Gravity The PE of the spring is added to both sides of the conservation of energy equation (KE + PE g + PE s )i = (KE + PE g + PE s )f Assuming that there is no nonconservative forces such as friction Example #5-39 The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed by x = 0.120 m and the gun fired vertically as shown, the gun can launch a 20.0 g projectile from rest to a maximum height of 20.0 m above the starting point of the projectile (x=0). (a) Find the spring constant, and (b) find the speed of the projectile as it moves through the equilibrium position of the spring.