Ch 09: Work and Kinetic Energy
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Problem 3
a. What is the angle Φ between vectors E and F in FIGURE P3.24?
Problem 3
The treasure map in FIGURE P3.41 gives the following directions to the buried treasure: 'Start at the old oak tree, walk due north for 500 paces, then due east for 100 paces. Dig.' But when you arrive, you find an angry dragon just north of the tree. To avoid the dragon, you set off along the yellow brick road at an angle east of north. After walking 300 paces you see an opening through the woods. In which direction should you walk, as an angle west of north, and how far, to reach the treasure?Problem 9
A particle moving on the x-axis experiences a force given by Fx = qx², where q is a constant. How much work is done on the particle as it moves from x=0 to x=d?Problem 9
(b) Doug uses a 25 N horizontal force to push a 5.0 kg crate up a 2.0-m-high, 20° frictionless slope. What is the speed of the crate at the top of the slope?Problem 9
T ─ (1500 kg) (9.8 m/s²) = (1500 kg) (1.0 m/s²) P = T (2.0 m/s) (a) Write a realistic problem for which this is the correct equation(s).Problem 9
A 1000 kg elevator accelerates upward at 1.0 m/s² for 10 m, starting from rest. (b) How much work does the tension in the elevator cable do on the elevator?Problem 9
A 150 g particle at x = 0 is moving at 2.00 m/s in the + x - direction. As it moves, it experiences a force given by Fₓ = (0.250 N) sin (x/2.00 m) . What is the particle's speed when it reaches x = 3.14 m ?Problem 9
The energy used to pump liquids and gases through pipes is a significant fraction of the total energy consumption in the United States. Consider a small volume V of a liquid that has density p. Assume that the fluid is nonviscous so that friction with the pipe walls can be neglected. (a) An upward-pushing force from a pump lifts this volume of fluid a height h at constant speed. How much work does the pump do?Problem 9
A pitcher accelerates a 150 g baseball from rest to 35 m/s. How much work does the pitcher do on the ball?Problem 9
A red ball has a mass of 250 g. A constant force pushes the red ball horizontally and launches it at a speed of 15 m/s . The same force pushes a green ball through the same distance, launching it at 25 m/s. What is the mass of the green ball?Problem 9
The cable of a crane is lifting a 750 kg girder. The girder increases its speed from 0.25 m/s to 0.75 m/s in a distance of 3.5 m. (a) How much work is done by gravity?Problem 9
A 35-cm-long vertical spring has one end fixed on the floor. Placing a 2.2 kg physics textbook on the spring compresses it to a length of 29 cm. What is the spring constant?Problem 9
A horizontal spring with spring constant 750 N/m is attached to a wall. An athlete presses against the free end of the spring, compressing it 5.0 cm. How hard is the athlete pushing?Problem 9
A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the engine and the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1480 kg, and two-thirds of the weight is over the drive wheels. (a) What is the maximum acceleration of the Porsche on a concrete surface where μₛ = 1.00 ? Hint: What force pushes the car forward?Problem 9
A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the engine and the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1480 kg, and two-thirds of the weight is over the drive wheels. (b) If the Porsche accelerates at aₘₐₓ, what is its speed when it reaches maximum power output?Problem 9
A Porsche 944 Turbo has a rated engine power of 217 hp. 30% of the power is lost in the engine and the drive train, and 70% reaches the wheels. The total mass of the car and driver is 1480 kg, and two-thirds of the weight is over the drive wheels. (c) How long does it take the Porsche to reach the maximum power output?Problem 9
How much work does tension do to pull the mass from the bottom of the hill (θ = 0) to the top at constant speed? To answer this question, write an expression for the work done when the mass moves through a very small distance ds while it has angle θ, replace ds with an equivalent expression involving R and dθ , then integrate.Problem 9
A 12 kg weather rocket generates a thrust of 200 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 550 N/m, is anchored to the ground. (a) Initially, before the engine is ignited, the rocket sits at rest on top of the spring. How much is the spring compressed?Problem 9
A 70 kg human sprinter can accelerate from rest to 10 m/s in 3.0 s . During the same time interval, a 30 kg greyhound can go from rest to 20 m/s . What is the average power output of each? Average power over a time interval ∆t is ∆E/∆t .Problem 9
A 90 kg firefighter needs to climb the stairs of a 20-m-tall building while carrying a 40 kg backpack filled with gear. How much power does he need to reach the top in 55 s?Problem 9
A farmer uses a tractor to pull a 150 kg bale of hay up a 15° incline to the barn at a steady 5.0 km/h . The coefficient of kinetic friction between the bale and the ramp is 0.45. What is the tractor's power output?Problem 9
(a) How much work does an elevator motor do to lift a 1000 kg elevator a height of 100 m? (b) How much power must the motor supply to do this in 50 s at constant speed?Problem 9
A gardener pushes a 12 kg lawnmower whose handle is tilted up 37° above horizontal. The lawnmower's coefficient of rolling friction is 0.15. How much power does the gardener have to supply to push the lawnmower at a constant speed of 1.2 m/s? Assume his push is parallel to the handle.Problem 9
At what speed does a 1000 kg compact car have the same kinetic energy as a 20,000 kg truck going 25 km/h?Problem 9
A mother has four times the mass of her young son. Both are running with the same kinetic energy. What is the ratio v(son)/v(mother) of their speeds?Problem 9
FIGURE EX9.20 is the force-versus-position graph for a particle moving along the x-axis. Determine the work done on the particle during each of the three intervals 0–1 m, 1–2 m, and 2–3 m.
Problem 9
A 2.0 kg particle moving along the x-axis experiences the force shown in FIGURE EX9.22. The particle's velocity is 3.0 m/s at x = 0m . At what point on the x-axis does the particle have a turning point?
Problem 9
An 8.0 kg crate is pulled 5.0 m up a 30° incline by a rope angled 18 ° above the incline. The tension in the rope is 120 N, and the crate's coefficient of kinetic friction on the incline is 0.25. (b) What is the increase in thermal energy of the crate and incline?Problem 9
Susan's 10 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30° above the floor. The tension is a constant 30 N and the coefficient of friction is 0.20. Use work and energy to find Paul's speed after being pulled 3.0 m.Problem 9
(a) How much work does an elevator motor do to lift a 1000 kg elevator a height of 100 m?
