Outcome 4 problem booklet

Outcome 4 Energy Monday Tuesday Wednesday Thursday Friday Notes and Videos – www.msbooth.ca ✔ Lessons Complete before 11.1 Mechanical Energy 11.2 Conservation of Mechanical Energy 12.1 Work 12.2 Power and Efficiency Concept Checks: •
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You must complete and self mark all concept checks for the outcome. Complete each concept check without referring to your notes or other resources. A calculator and a formula sheet are permitted. When you are done, see your teacher for the answer key. Mark your concept check with a colored marking pen or pencil and write down corrections. Concept Check Checklist Concept Check Lesson 11 Lesson 12 ✔ ✔ Marked Completed Lesson 11 Practice Problems 1) A 0.75 kg ball is rolling at a speed of 5.4 m/s. Calculate the kinetic energy. (11 J) 2) A 450g bird is flying 12 km/h. Calculate the kinetic energy. (2.5 J) 3) A 62 kg astronaut floats through space with 194J of energy. Calculate her speed. (2.5 m/s) 4) A man is running at 7.2 km/h with 150 J of energy. What is his mass? (75 kg) 5) A 0.95 kg hammer is 1.1 m above a nail. Calculator the hammers gravitational potential energy. (10J) 6) If a 5.2 g object has a gravitational potential energy of 100.0 J. How high above the ground is the object? (2.0x103 m) 7) At a point in time, a 5.5 kg cannon ball is 5.6m above the ground and travelling at a speed of 23 m/s. Calculate its kinetic energy. (1.5x103 J) 8) A 0.5 kg ball that is thrown in the air at a point in time has 20 J of potential energy and 40 J of kinetic energy. Here is a bar that describes the energies (kinetic, gravitational potential and mechanical) at this point in time. a) Draw the bar graph to describe the ball’s energy at a moment later when the balls potential energy is 30 J. b) Draw the bar graph to describe the ball’s energy at a moment later when the balls speed is 14 m/s. 9) A 1.6 kg ball is 4.2 m above the ground. a) At the instant it is released, what is its gravitational energy? b) At the instant before it hits the ground what is its kinetic energy and speed? (66 J, 66 J, 9.1 m/s) 10) In the previous question calculate the total mechanical energy at a height of 4.2m, 2.1m and 1m. 11) A 90 g paper airplane has a mechanical energy of 75.0 J when it is 12.5 m from the ground. How fast is it flying? (37.7 m/s) 12) A roller coaster vehicle with occupants has a mass of 2.9 x 103 kg. It starts at point A with a speed of 14 m/s and slides down the track through a vertical distance of 25 m to B. It then climbs in the direction of point C which is 36 m above B. An interesting feature of this roller coaster is that due to cost-­‐over-­‐runs and poor planning, the track ends at point C. The occupant is the chief design engineer of the roller coaster ride. Estimate the speed of the vehicle at point B and then determine whether the fellow survives the ride. (26 m/s) 13) A roller coaster is shown in the drawing. Assuming no friction, calculate the speed at points B, C, D, assuming it has a speed of 1.80 m/s at point A. (24 m/s, 10 m/s, 19 m/s) 14) A motorcycle rider is trying to leap across the canyon as shown in the figure by driving horizontally off the cliff. When it leaves the cliff, the cycle has a speed of 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side. (46.2 m/s) 15) A 6.00 m rope is tied to a tree limb and used as a swing. A person starts from rest with the rope held in a horizontal orientation, as in the figure. Ignoring friction and air resistance, determine how fast the person is moving at the lowest point on the circular arc of the swing. (10.8 m/s) Lesson 11 Concept Check 1) The roller coaster to the right has the following properties: Mass of car = 500 kg Height of point A = 150 m Height of point B = 75 m Height of point C = 10 m Height of point D = 85 m The roller coaster track is frictionless a) If the velocity at point A is 25 m/s, what is the kinetic energy at point A? b) What is the mechanical energy at point A? c) Use the law of conservation of energy to determine the kinetic energy at points B, C and D. d) What is the speed of the roller coaster at points B, C and D? 2) In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy. With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.10 m and cross the bar with a speed of 0.80 m/s? Lesson 12 Practice Problems 1) Can work be done on an object that remains at rest? Explain. 2) A train traveling at a constant speed makes a 180° turn on a semicircular section of track and heads in a direction opposite to its original direction. Even though a (centripetal) force acts on the train, no work is done. Why? 3) A book at one end of a table is lifted up into the air. The book is then moved to the other end of the table and lowered onto the table. Explain why no net work was done on the book. 4) The cable of a large crane applies a force of 2.2 x 104 N to a demolition ball as the ball is lifted vertically a distance of 7.6 m. How much work does this force do on the ball? Is this work positive or negative? Explain. (+1.7 x 105 J) 5) Fred is moving into an apartment at the beginning of the school year. Fred weighs 685 N and his belongings weigh 915 N. How much work does the elevator do in lifting Fred and his belongings up five stories (15.2 m)? How much work does the elevator do on Fred on the downward trip? (+2.43 x 104 J, -­‐1.04 x 104 J) 6) The drawing below shows a boat being pulled by two locomotives through a two kilometre canal. The tension in each cable is 5.00 x 103 N and θ= 20o. What is the work done on the boat by the locomotives? (1.88 x 107 J) 7) Given the following force-­‐displacement graphs, determine the work done in each case. (56 J, -­‐26 J) 8)
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A 2.40 x 102 N force, acting at 20° above the surface, is pulling on an 85.8 kg refrigerator across a horizontal floor. The frictional force opposing the motion is 1.67 x 102 N and the refrigerator is moved a distance of 8.00 m. Find the work done by the applied force and the work done by the frictional force. (1.80 kJ, 1.34 kJ) A window washer on a scaffold is hoisting the scaffold up the side of a skyscraper by pulling down on a rope. The combined mass of the window washer and the scaffold is 155 kg. If the scaffold is pulled up at a constant velocity through a distance of 120 m. How much work was done? (1.82 x 105 J) 10) An 80.0 kg box is pushed up a frictionless incline as shown in the diagram. How much work is done on the box in moving it to the top? (5.49 kJ) 11) If a 4.00 kg board skidding across the floor with an initial speed of 5.50 m/s comes to rest, how much thermal energy is produced? (60.5 J) 12) One of the fastest roller coasters (2000 kg) in the world is the Magnum XL -­‐ 200 at Cedar Point Park in Sandusky, Ohio. This ride includes an initial vertical drop of 59.3 m. Assume that the roller coaster has a speed of nearly zero as it crests the top of the hill. a) If the track was frictionless, find the speed of the roller coaster at the bottom of the hill. (34.1 m/s) b) The actual speed of the roller coaster at the bottom is 32.2 m/s. If the length of track is 125 m, what is the average frictional force acting on the roller coaster? (1.01 x 103 N) 13) The speed of a hockey puck (mass = 100.0 g) decreases from 45.00 m/s to 42.68 m/s in coasting 16.00 m across the ice. a) How much thermal energy was produced? (10.17 J) b) What frictional force was acting on the puck? (0.6357 N) 14) A 75 g arrow is fired horizontally. The bow string exerts an average force of 65 N on the arrow over a distance of 0.90 m. With what speed does the arrow leave the bow string? (39 m/s) 15) **For the pulley system illustrated to the right, when the masses are released, what is the final speed of the 12 kg mass just before it hits the floor? (7.0 m/s) Power 16) What is the power output of a machine which applies a force of 2.50 x 104 N for 12.0 s in pulling a block through 60.0 m? (125 kW) 17) A machine has an output power of 10.0 kW. How long would it take for the machine to raise a 5000 kg load through a height of 2.5 m? (12.3 s) 18) Water flows over a section of Niagara Falls at the rate of 1.2 x 106 kg/s and falls 50.0 m. How much power is generated by the falling water? (5.9 x 108 W) 19) A machine operates at a power consumption of 3.5 kW for ten minutes. In the process it produces 500 kJ of waste heat energy. How much net work was done? (1.6 MJ) Lesson 12 Concept Check 1. During an automobile accident investigation, a police officer measured the skid marks left by a car (mass = 1500 kg) to be 65 m long. If the frictional force on the car was 7.66 kN during the skid, was the car going faster than the 100 km/h speed limit before applying the brakes? (slower) 2. A 10 kg box is placed at the top of this incline and allowed to slide down. The force of friction on the box as it travels along the surface of the incline is 11 N and the height (h) is 3.5 m. Use your understanding of work and mechanical energy to determine the speed of the box when it reaches the bottom. 1. What is the efficiency of the incline in the question above? 2. If a 11 mW light bulb is left on for 20 minutes, how much energy does it burn?