Re-read Chapters 7 and 8 from your text. Read for the first time chapter 5.

Some quick review questions:

  1. How much momentum in a 6 kg cart traveling 2 m/s? p = mv 6 • 2 = 12 kg•m/s
  2. How much impulse from a 3 N force exerted for 9 s? ∆p = F•t = 3 • 9 = 18 N•s27 N•s
  3. How much kinetic energy in a 2 g mass traveling 3 m/s? Ek = .5 • 2.002 kg• 3•3 = .009 J
  4. How much gravitational potential energy in a 4 kg mass held 3.0 meters above the floor (our chosen reference point)? Ep = mgh = 4 • 10 • 3 = 120 J
  5. What is the spring constant where a spring with natural length 0.40 meters stretches to 0.60 meters under the influence of a 5.0 N force? k = F/∆x = 5 N÷0.2 m = 25 N/m
  6. How much energy is stored in a spring where the spring constant is 2.0 N/m and the spring has been stretched from a natural length of 1.7 m to an elongated 2.2 meters? Es = .5 • 2 • .5 •.5 = .25 J
  7. What is the average speed of an object if it goes 45 meters in 5 seconds? v = 45 m/5 s = 9 m/s
  8. What's the rate of acceleration for an object that travels 3 m/s at one instant then accelerates uniformly to a speed of 12 m/s over the next 6 seconds? a = ∆v/t = 9 m/s ÷ 6 s = 1.5 m/s/s
  9. How far does an object travel between the 5th second and the 8th second if it accelerates uniformly from rest at a rate of 4 m/s/s for 10 seconds? It's going 20 m/s at 5 s and 32 m/s at 8 seconds, so the average is 26 m/s for the 3 second span: 26 •3 = 104 78 m
  10. How much work is done by a 50 N force exerted over a distance of 3.5 meters? 50 • 3.5 = 175 J

Now a more interesting series of questions:

  1. Sketch the graph of force vs. time for a 12 Newton force that works without interuption for 8 seconds (place force on the y-axis). It's not necessary to use graph paper, a very rough sketch should do it. The question is this: what common geometric shape does this graph produce? It's a rectangle.
  2. What is the area of that figure? Include units in your answer. These units are consistent with what physics quantity? 12 N • 8s = 96 N•s (impulse, or change in momentum)
  3. Sketch another graph. This time the force begins at 0 and increases at constant rate until it is 24 N at the 8 second mark. What common geometric shape does this produce? It's a triangle.
  4. What is the area of that figure? 0.5 • 24 N • 8s = 96 N•s
  5. Make a generalization: "the area enclosed by the graph of a force vs. time graph is equal to the ____change in momentum that results_________________."

So Isaak Newton has this goat cart. It has a mass of 250 kg loaded.

  1. If the goats pull with a net force of 100 N for the first 5 seconds, how fast will the cart be travelling? m∆v = F•t so m∆v = 100 N • 5 s = 500 N•s; ∆v therefore = 500 ÷ 250 kg = 2 m/s.
  2. How much work was done on the cart during that period of time? W = ∆E = .5 • 250 •2 • 2 = 500 J (the kinetic energy of the cart at 2 m/s)
  3. If the coefficient of rolling friction between the cart's wheels and the road (plus some at the axles) is 0.15, how hard will the goats have to continue to pull to maintain that speed (from number 1)? Ff = µFN = µmg = .15 • 250 kg • 10 m/s/s = 375 N (so the net force of 100 N in number 1 means they actually pulled at 475 N of total force)
  4. So how much additional work for the goats to pull the cart 5 km along a level road to market? 375 N • 5000 m = 1,875,000 J.
  5. If the goats bring the cart from rest to 12 m/s over 40 seconds, what net force is required? (Use the definition of force as the rate of change of momentum: F = ∆p/t). ∆p = m∆v = 250 kg • 12 = 3000 kg • m/s. 3000 kg • m/s ÷ 40 seconds = 75 N of net force.