Download SPH4U: Course Outline

SPH4U: Energy and Momentum Review
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p  mv
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p  Ft  mv
W  Fd cos
F  kx
Ek  12 mv2
Ee  12 kx2
E g  mgh
W  Ek
Test Format: Multiple Choice (12 marks), Short Answer (28 marks), Total – 40 marks
Topic
Textbook Questions (previously assigned)
Momentum and Impulse
p. 237 - #6, 7, 10; p. 243 - #5, 7, 8
Types of Collisions, Energy and Momentum in Collisions
p. 248 - #5; p. 251 - #11, 12, 13
Conservation of Momentum in 1D, in 2D
p. 257 - #3, 4abd, 5
Work-Energy Theorem, Types of Work
p. 181 - #5, 7; p. 186 - #4, 6, 10
Gravitational Potential Energy, Kinetic Energy,
Conservation of Energy
p. 191 - #1, 4; p. 197 - #6; p. 200 - #13; p. 201 - #6
Hooke’s Law, Elastic Potential Energy
p. 206 - #5; p. 211 - #10, 12
Key Ideas:
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Impulse-Momentum Theorem: the momentum for an object can be changed by an impulse (a force applied
over time).
Conservation of Momentum: the momentum of a system (e.g. 2 colliding objects) is conserved in all
collisions where Fnet=0, but Ek and total mechanical energy (Ek + Eg) is conserved only in elastic collisions.
2D collision problems can be broken down into conservation of momentum in x- and y-directions.
Work is done on an object when its energy is changed. This requires that a force be applied to an object,
causing a displacement in the direction of a component of the applied force.
Work-Energy Theorem: If an object’s potential energy does not change, the work done on the object is
equal to its change in kinetic energy.
Conservation of Energy: If no external work is done on a system (e.g. friction, energy lost as heat or sound),
then mechanical energy (Ek + Eg) is conserved.
An energy bar chart could be helpful to visualize the forms of energy a system has at 2 different points in
time.
Hooke’s Law: The force exerted by a spring is proportional to the amount that the spring is compressed or
stretched from its equilibrium position.
Elastic potential energy Ee is another form of potential energy to be considered in conservation of energy
problems.
Review Questions:
1. A 19 kg curling stone is sliding along the ice at 4.6 m/s [E 10° S] when an errant hockey puck (170 g)
traveling at 20 m/s [N 35° E] strikes it. After the collision, the curling stone continues on at 4.56 m/s [E
6.8° S]. Determine the velocity of the hockey puck immediately after the collision. What kind of collision is
this?
2. You apply a horizontal force of 40 N to push a 10 kg shopping cart from rest to a speed of 1.5 m/s in 2.0 m.
(a) How much work have you done?
(b) Using the Work-Energy Theorem, determine the amount of work done on the shopping cart.
(c) Using your answer from (b), determine the net force on the cart.
(d) How much work was done by friction?
(e) Calculate the net force using Newton’s 2nd Law and the Big FIVE and compare your answer to (c).
3. In yet another mishap in his misguided mission to make a meal of the Roadrunner, Wile E. Coyote (50 kg)
flies horizontally through the air towards a brick wall. A conveniently placed spring (k = 5000 N/m)
compresses 0.75 m and brings him to a complete stop in 0.45 s.
(a) What is the maximum force exerted by the spring on the coyote?
(b) Assuming that the force exerted by the spring increases linearly with time, sketch a graph of the spring
force as a function of time from first contact until the coyote comes to a stop.
(c) Using your graph, find the coyote’s change in momentum.
(d) What was the coyote’s speed when he first came in contact with the spring?
4. (p. 202 - #10) A box of apples of mass 22 kg slides 2.5 m down a ramp inclined at 44˚ to the horizontal. The
force of friction on the box has a magnitude of 79 N. The box starts from rest.
(a) Determine the work done by the friction.
(b) Sketch an energy bar chart for the box at the top of the ramp and at the bottom of the ramp.
(c) Use your bar chart from (b) to write an equation for conservation of energy and determine the final speed
of the box.
5. A certain amphibian (25 kg) jumps vertically up off a platform 3.5 m high with an initial speed of 2.0 m/s,
but fortunately lands in (and sticks to) a 50 kg marshmallow pit whose surface is level with the ground. The
marshmallow is attached to a vertical spring, which compresses 20 cm before the amphibian is brought to a
stop.
Using energy and momentum techniques only:
(a) Sketch an energy bar chart for the amphibian at the top of the platform and just before contact with the
marshmallow. Determine the speed of the amphibian just before contact with the marshmallow.
(b) Determine the speed of the amphibian and marshmallow immediately after impact.
(c) Sketch an energy bar chart for the amphibian just after contact with the marshmallow and at maximum
spring compression. Determine the spring constant (in N/m). Don’t forget that there is also a change in
gravitational potential energy when the spring compresses!
Answers:
1. 17.2 m/s [E 45.9° S], inelastic
2. (a) 80 J, (b) 11.3 J, (c) 5.6 N, (d) -68.8 J, (e) 5.6 N
3. (a) 3750 N, (c) -8.4 × 102 kg m/s, (d) 1.7 × 101 m/s
4. (a) -2.0 × 102 J, (c) 4.0 m/s
5. (a) 8.5 m/s, (b) 2.8 m/s, (c) 2.2 × 104 N/m