Energy& Momentum ~Learning Guide Name: Instructions: Using a pencil, answer the following questions. The Pre-Reading is marked, based on effort, completeness, and neatness (not accuracy). The rest of the assignment is marked, based on effort, completeness, neatness, and accuracy. Every time you see a bold word, make sure you refer back to your "Submission Requirements." Do your best! 1. Work is scalar (W= Fd). However, we have seen that F and d must be parallel for work to be done. This would mean that we have to use components. i. What does it mean to be scalar? Vector? ii. Even though we use parallel components, why is it still a scalar? 2. Bank accounts are similar to work. Assets are considered to increase your wealth while deficits decrease it. Accountants look at both of these to decide your net wealth. Net wealth can be in many forms (stocks, bonds, cash, real-estate, etc). Describe how work is similar to this accounting analogy. Be sure to discuss deficits and assets and Net Work. Page 1 of 23
3. In the figures below, identical boxes of mass 10 kg are moving at the same initial velocity to the right ona flat surface. The same magnitude force, F, is applied to each box for the distance, d, indicated in thefigures. Rank these situations in order of the work done on the box by F while the box moves the indicateddistance to the right. Greatest 1 2 3 4 5 6 Least Or, all of the boxes experience the same work. Please carefully explain your reasoning. Page 2 of 23
4. A 50 kg crate is pushed with a force, F, of 40 N over two different surfaces. The first 10 m is over ice (frictionless) and the last 10 m is a rough surface where the friction coefficient is 0.2. i. Work is defined as a change in energy of an object. In Physics 12 we talk about kinetic energy, gravitational potential energy, and thermal energy. What two forces are contributing to the overall energy of the crate? Discuss whether they are positive or negative contributions to the overall energy of the crate. ii. How much work was done on the crate have after the first 10 m? What type of energy is this manifested as? (ans: 400 J) iii. Determine the velocity of the crate at point A in the diagram. (ans: 4 m/s) iv. Determine the force of friction. How does this force compare to F? Describe the motion of the crate between points A and B. (ans: F f = 98 N) Page 3 of 23
v. The crate will come to rest between points A and B. Using the work-energy theorem determine the distance past point A at which the crate comes to rest. Remember, we want the Net Work done on the crate to be equal to -400J (i.e. we wish to now remove the kinetic energy that the crate has at point A) (ans: 6.9 m) 5. Define Power as a rate. Describe exactly what it means in terms of energy and time when a hairdryer is rated at 750 W. 6. Show that a kw h is actually a unit of energy with the use of equations and dimensional analysis (LOOKING AT THE UNITS). Determine the conversion between kw h and J. (ans: 3.6 x 10 6 J) 7. Derive the equation P = Fv for objects moving at a constant speed. Start with the general equation for power. Page 4 of 23
8. A motor using 3.7 x 10 3 W is 81% efficient. This motor is pulling a 450 kg block along a horizontal surface at a steady speed. If the coefficient of friction is 0.35, what is the speed of the block?(ans: 1.94 m/s) Conservation of Energy: 1. A water slide is made so that swimmers, starting from rest at the top, leave the end of the slide travelling horizontally as shown. One person is observed to hit the water at a horizontal distance of 6.0 m from the end of the slide 0.45 s after leaving the slide. The effects of friction and air resistance are negligible. a. Describe the energy transformations involved from the top of the slide to the bottom. b. From what vertical height, h, did the person start?(ans: 9.1 m) Page 5 of 23
2. Another slide has the same vertical height, h, as the original slide, but has a much steeper slide angle. The same person from above is observed to go down this steep slide. Using principles of physics (in particular energy), explain how the new horizontal distance from the edge of the slide compares with the first situation when a. The effects of friction and air resistance are negligible. b. The effects of friction and air resistance count. Page 6 of 23
3. Pulley Problem revisited: Earlier in the dynamics unit we studied the physics of gravity-powered pulley problems such as blocks depicted below. a. The two masses in the pulley system shown are initially at rest. After they are released, the hanging mass, B, falls through a height of 0.80 m and hits the floor. Assume friction is negligible and describe in words the energy transformations involved in this system. Be sure to state the initial energy state and the final. b. Write out the conservation of energy equation you would use to solve this question. Please use the variables depicted in the diagram along with g. Page 7 of 23
c. What is the speed of the masses just before B strikes the floor?evaluate your answer to part (a) for the case where m A =6.0 kg, and m B =4.0 kg.show all work. (ans. 2.5 m/s) 4. Resolve this question using what we learned in dynamics and kinematics (remember: the link between dynamics and kinematics is acceleration). 5. A pendulum bob is has a 2m long string attached to a 0.5 kg mass. It is released at an angle of 30 to the vertical. a. Draw a sketch showing the angles. Use the sketch to determine the launch height. Show all work(ans. 0.27 m). b. How fast is the pendulum moving at the bottom, of the swing? (ans: 2.3 m/s) Page 8 of 23
6. Jane (60 kg) grabs a rope 10 m long and swings on the end of it, like a pendulum. Her starting point is on the platform shown. How fast is Jane moving as she passes through the bottom of the swing? Show all work (ans. 14 m/s). i. The first question is one of geometry. Show that Jane will clear the rocky ledge that is 5m above the water. Jane has pre-measured the position of this rock to be 2.5 m horizontally to the left of the platform. ii. At the bottom of the swing her speed is found to be 12 m/s. How much energy was lost? (ans: 1560 J) Page 9 of 23
7. An electric motor and a rope are used to pull a 10 kg crate of car parts up an inclined plane as shown below. The crate starts out from rest on the ground and ends up with speed v f at a height of 4.0 m above the ground. The graph below shows the force exerted on the crate by the motor as it is pulled 10 m up the inclined plane. a. Using the graph above, determine the work done on the crate by the motor. Show that the units for your calculation are equivalent to the units for work. (ans: 575 J) b. During the crate s ascent up the ramp it heats up. Since W = ΔE, discuss the type(s) of energy that is given to the crate through this process. c. The thermal energy produced amounts to 150 J. Use your answer above to determine the final velocity of the crate. (ans: 2.6 m/s) Page 10 of 23
Momentum and Impulse in 1D Review: 1. A space vehicle made up of two parts is travelling at 230 m/s as shown. An explosion causes the 450 kg part to separate and travel with a final velocity of 280 m/s as shown. a. Is this considered to be elastic or inelastic? Look up these definitions and support your decision with these. b. For ANY collision or explosion what two quantities are ALWAYS conserved? Be specific. c. After the explosion shown above we see that the front nose increases its velocity from 230 m/s to 280 m/s. What do you predict will happen to the rear of the space vehicle? How does your prediction support your answer to (b) above? d. Determine the final velocity of the rear piece. (ans: 211.25 m/s) Page 11 of 23
e. Calculate the change in momentum of both the front a rear pieces separately. Be careful with the signs. What did you discover for explosions (and collisions) involving two masses?(ans: 22500 kg m/s) f. What is the Impulse that acts on each piece during the explosion? Use above to help. g. Explain why your answers to (f) make sense if we consider the equation I = F avg t as opposed to I = Δp. Be sure to refer to the appropriate of Newton s Laws to assist in your explanation (no calculations are necessary). 2. The graph below shows the force acting on a tennis ball (mass 0.055 kg) as a function of time. a. Determine what the units would be for the area under the curve. What does this area represent (pay attention to the units)? Page 12 of 23
b. Do your best to estimate the area under this curve by counting squares and partial squares. (ans: approx. 1 N s) c. What is the impulse given to the ball? d. Assuming the ball was initially at rest, what was the final speed of the ball after the force acted on it? (ans: approx.. 18.1 m/s) e. Determine the average Force that acts on the ball over this time interval. Draw a horizontal line on the graph at this point and label it F avg. (ans: approx. 143 N) 3. A 0.05 kg bullet moving vertically upwards at 125 m/s hits a stationary 2.6 kg block hanging from a 5.00 m long string. The block then soars upward until it reaches a maximum height (you may assume that the bullet remains within the sandbag). a. What physics concept applies for the collision between the bullet and the block? Calculate the speed the block has immediately after the collision. (ans: 2.36 m/s) Page 13 of 23
b. What kind of energy does the block have after the collision? Where does this energy go once it soars into the air and reaches its maximum height? c. Calculate the maximum height reached by the block. (ans: 0.28 m) 4. When stunt men jump off a high ledge or building they always roll upon impact. Explain the necessity of this maneuver using the physical laws that support collisions. 5. Compare the total kinetic energy before and after for each of the situations below. Discuss what happens to the energy. Situation Elastic collision Total kinetic energy after (compared to before) circle choice Increases / decreases / same If there is a change in Kinetic Energy where does this energy go or come from? Inelastic collision Increases / decreases / same Explosion Increases / decreases / same 6. Discuss why there are no seatbelts in a passenger train. What would happen to the passengers if the train were to collide with a car on the tracks? Page 14 of 23
7. The figures below depict carts moving along a horizontal surface at the speeds specified. The masses of the carts vary; specific values are given in the figures. The carts hit, compress the springs to some maximum amount, and then rebound. All of the spring systems are identical, exerting the same average force on the carts, and the carts all hit the springs exactly the same way. The carts are not self-propelled, so they compress the springs for some maximum amount of time before stopping. Rank the situations in order from the greatest time of compression to the least time of compression. That is, put first the cart that takes the longest time to reach maximum compression, and put last the cart that takes the shortest time. Greatest 1 2 3 4 5 6 7 8 Least Or, all carts will stop in the same amount of time. Carefully explain the reasoning behind your ranking. Page 15 of 23
Momentum and Impulse 2D questions 1. A billiard ball will stop short when it collides head-on with a ball at rest. The ball cannot stop short, however, it the collision is not exactly head on--that is, if the second ball moves at an angle to the path of the first. Momentum is ALWAYS conserved. Explain how momentum would be conserved in this two dimensional collision. You may use a diagram drawn to scale and labelled with the appropriate angles, or you may use a component argument. We are looking to see how one might solve such a question. Page 16 of 23
2. Conservational are often expressed as something before = something after. However, they can often be expressed as a give and take equation where something is gained at the expense of something lost. For example, conservation of energy (imagine this for a swinging for a pendulum) can be written as E pi + E ki = E pf + E kf E pi E pf = E kf E ki -(E pf E pi ) = E kf - E ki -ΔE p = ΔE k (equation 1) OR, if we rewrite i. Express, in your own words, what equation 1 above is telling us about energy transformations as a pendulum swings back and forth? ii. Write the conservation of momentum equation (for a collision involving only two masses) as we did above so that changes in momentum are represented. iii. What does your equation above tell you about the Impulse that each mass will experience? Show any formulas involved. Page 17 of 23
3. A stationary 20.0 kg mass explodes into three fragments. As shown in the diagram below, the 5.0 kg fragment moves north with an initial speed of 7.0 m/s. The 9.0 kg fragment moves off at 38 S of W with an initial speed of 4.0 m/s. a. What must the total momentum for all three pieces be after the explosion? State the law that justifies your answer. b. Any collision or explosion must adhere to the Law of Conservation of Energy. Collisions that are perfectly elastic are ones in which Kinetic Energy is Conserved. Is it possible for an explosion such as this to be elastic? Is kinetic energy gained or lost? Briefly explain. c. State how energy is conserved in an explosion like this? Be specific. Page 18 of 23
d. What is the velocity (magnitude and direction) of the 6.0 kg fragment after the explosion? Solve this question using both the trigonometric and the component methods. (ans: 5.19 m/s at 66 east of south) Trig. Method (include a vector diagram) Component Method (show all work) Page 19 of 23
4. A 98.0 kg hockey player skating at 2.12 m/s 32 S of W is body checked by an 87.0 kg opponent who is skating at 1.40 m/s 42 N of E. They collide inelastically and stick together. a. What is the velocity of the pair immediately after the collision? Solve using both methods.. (ans: 0.488 m/s 18.5 S of W) Trig. Method (include a vector diagram) Component Method (show all work) Page 20 of 23
b. Determine the impulse imparted to the 98.0 kg player. Show a complete vector diagram and label your answer. (ans: 161.8 kgm/s at 36.1ºN of E) c. From what you know about Impulse, what would the Impulse for the 87.0 kg player be? Provide both magnitude and direction. (you need not calculate if you understand the concepts) d. State what you found out for questions b and c above and justify your results using I = F avg t. State any of the appropriate Newton s Laws to help explain. No calculations are necessary. Simply justify what you found out from (b) and (c) by using the other equation for Impulse, I = F avg t. Page 21 of 23
5. Refer to the tutorial on Impulse in 2D to answer the questions below: a. A Force vs. time graph was created for two different balls above as they collided with the floor. Both balls had the same mass and initial velocity. The shapes of the graphs were as follows: Page 22 of 23
State the how the physical characteristics of each ball may have accounted for the shapes of the graphs above. Be sure to describe how each physical property would affect the curve and why. Graph (a) Characteristics of the ball Effect on the Curve (and why) Graph (b) Characteristics of the ball Effect on the Curve (and why) b. Redraw each graph (a) and (b) from the point of view of the forces experienced by the floor. Page 23 of 23