Solve the following problems. Remember to show all work and employ proper problem-solving techniques including equations, substitutions, and units.
W = Fapplied x d PEgravitational = m x g x h KEmechanical = (mvexp2)/2 P = W/t PEelastic = (kxexp2)/2
Law of Conservation of Energy: The total energy of a system always remains constant. Work-Energy Theorem: Wnet = DKE = KEfinal - KEinitial
1. How much work is required to accelerate a 1000. kg car from rest
to 5.00 m/s?
2. How much work is required to accelerate a 1000. kg car from rest up to 10.0 m/s?
3. How much work is required to accelerate a 1000. kg car from
10.0 m/s to 20.0 m/s?
4. If the force applied to accelerate the car in questions 2 and 3 was 500. N, calculate the respective distances over which the force was applied in each situation.
5. Calculate the impulse applied to the car in questions 2 and 3, respectively.
6. A 0.20 kg baseball covers a distance of about 1.00 meter being accelerated from rest to 30. m/s by a pitcher. (A) How much work is done by the pitcher on the ball? (B) Calculate the average force exerted on the ball by the pitcher. (C) Calculate the pitcher's power output in watts and horsepower.
7. Consider a 2000 kg car traveling at 22.0 m/s. (A) Calculate the car's KE. (B) How much work must be done by friction in stopping the car? (C) If the average force of friction during braking is 2,000 N, how far will the car travel before stopping?
8. Electric energy is sold to the public by the "kilowatt-hour" rather than by the joule. A kilowatt-hour is the amount of energy needed to run a 1 kilowatt appliance for 1 hour. (A) Show that 1.0 kW-h = 3,600,000 joules. (B) Lets say that the typical family uses electrical power at an average daily rate of 500 watts (averaged throughout the day and night). Electricity costs 12 cents/kW-h. Calculate the cost of an average monthly electric bill for a typical family.
9. (A) How much work must be done to compress a spring of
k = 1000. N/m a distance of 5.00 cm? (B) As it is being compressed, how much work is the spring doing? Is the force exerted by the spring during this time constant or varying? (C) If the spring is compressed 5.00 cm in response to a 0.500 kg mass and then allowed to be released, with what velocity will the mass leave the spring?
10. A swinging pendulum which consists of a 200. g bob attached to a 1.00-m-long wire reaches a height of 10.0 cm above base level. There is no air resistance to the bob's motion. (A) Calculate the bob's PE at its maximum height. (B) Calculate the bob's KE at base level.
(C) Calculate the bob's speed at base level. (D) Calculate the bob's speed at 5.0 cm above base level.
11. A 250 kg roller coaster begins its journey with an initial velocity of 5.00 m/s on a horizontal track at a height of 100.0 m. The track then descends to another horizontal stretch of track that is 20.0 m high. The track then forms a complete circular loop tangent to the lower horizontal track with a radius of 25.0 m. The track then rises to a final horizontal stretch with a height of 40.0 m. (A) Calculate the total mechanical energy of the coaster at the start of its journey. (B) Calculate the PE of the coaster at the 20.0 m high track, the top of the loop, and the end of its journey. (C) Calculate the KE of the coaster at the 20.0 m high track, the top of the loop, and the end of its journey. (D) Calculate the speed of the coaster at the 20.0 m high track, the top of the loop, an the end of its journey.
12. Let's assume that 80,000 joules of energy is lost to friction between the start and the end of the coaster's journey expressed in question 11. (A) Calculate the KE of the coaster at the end of the journey. (B) Calculate the final speed of the coaster. (C) If the total length of the track is 400. m, calculate the average force exerted on the coaster during this time. (D) Estimate the coefficient of friction between the coaster and the track.
13. A 17.0 kg child travels down a playground slide 3.50 m high and reaches the bottom with a speed of 2.50 m/s. How much heat was generated due to friction as a result of this process?