Solved: Can kinetic energy ever be negative? Can

How do interactions affect energy?

What is potential energy?

When is energy conserved?

What is an energy diagram?

How is force related to potential energy?

Where are we now in our study of energy?

Rafael uses a slingshot to shoot a 25 g pebble straight up at 17 m/s. How high does the pebble go?

A 5.0 kg watermelon is dropped from a third-story balcony, 11 m above the street. Unfortunately, the water department forgot to replace the cover on a manhole, and the watermelon falls into a 3.0-m-deep hole. How fast is the watermelon going when it hits bottom?

Two identical projectiles are fired with the same speed but at different angles. Neglect air resistance. At the elevation shown as a dashed line, a. The speed of A is greater than the speed of B. b. The speed of A is the same as the speed of B. c. The speed of A is less than the speed of B

Christine runs forward with her sled at 2.0 m/s. She hops onto the sled at the top of a 5.0-m-high, very slippery slope. What is her speed at the bottom?

A small child slides down the four frictionless slides ad. Each has the same height. Rank in order, from largest to smallest, her speeds va to vd at the bottom.

During the skateboard finals, Isabella encounters a 6.0-m-long, 15 upward ramp. Isabellas mass, including the skateboard, is 55 kg, and the coefficient of rolling friction between her wheels and the ramp is 0.025. With what speed must she start up the ramp to reach the top at 2.5 m/s? What percentage of her mechanical energy is lost to friction?

A skier glides down a gentle slope at constant speed. What energy transformation is taking place? a. UG S K b. UG S K + Eth c. UG S Eth d. K S Eth e. No energy transformation is occurring

In a laboratory experiment, your instructor challenges you to figure out how fast a 500 g air-track glider is traveling when it collides with a horizontal spring attached to the end of the track. He pushes the glider, and you notice that the spring compresses 2.7 cm before the glider rebounds. After discussing the situation with your lab partners, you decide to hang the spring on a hook and suspend the glider from the bottom end of the spring. This stretches the spring by 3.5 cm. Based on your measurements, how fast was the glider moving?

A spring-loaded pop gun shoots a plastic ball with a speed of 4 m/s. If the spring is compressed twice as far, the balls speed will be a. 2 m/s b. 4 m/s c. 8 m/s d. 16 m/s

A particle with the potential energy shown in the graph is moving to the right. It has 1 J of kinetic energy at x = 1 m. Where is the particles turning point?

Your lab assignment for the week is to devise an innovative method to determine the spring constant of a spring. You see several small blocks of different mass lying around, so you decide to measure how high the compressed spring will launch each of the blocks. You and your lab partners realize that you need to compress the spring the same amount each time, so that only the mass is varying, and you choose to use a compression of 4.0 cm. You decide to measure height from the point on the compressed spring at which the block is released. Four launches generate the data in the table: Mass (g) Height (m) 50 2.07 100 1.11 150 0.65 200 0.51 What value will you report for the spring constant?

A particle moves along the x-axis with the potential energy shown. The x-component of the force on the particle when it is at x = 4 m is a. 4 N b. 2 N c. 1 N d. -4 N e. -2 N f. -1 N

A pendulum is created by attaching one end of a 78-cm-long string to the ceiling and tying a 150 g steel ball to the other end. The ball is pulled back until the string is 60 from vertical, then released. What is the speed of the ball at its lowest point?

A spring of length L0 and spring constant k is standing on one end. A block of mass m is placed on the spring, compressing it. What is the length of the compressed spring?

A weight attached to a rope is released from rest. As the weight falls, picking up speed, the rope spins a generator that causes a lightbulb to glow. Define the system to be the weight and the earth. In this situation, a. U S K + Wext. Emech is not conserved but Esys is. b. U + Wext S K. Both Emech and Esys are conserved. c. U S K + Eth. Emech is not conserved but Esys is. d. U S K + Wext. Neither Emech nor Esys is conserved. e. Wext S K + U. Emech is not conserved but Esys is.

A systems potential energy is given by U1x2 = 12x3 - 3x2 2 J, where x is a particles position in m. Where are the equilibrium positions for this system, and are they stable or unstable equilibria? SOLVE You learned in Chapter 6 that a particle in equilibrium has F u net = 0 u . Then, in the previous section, you learned that the maxima and minima of the PE curve are points of equilibrium.

A mountain climber uses a rope to drag a bag of supplies up a slope at constant speed. Show the energy transfers and transformations on an energy bar chart.

An exercise machine at the gym has a 5.0 kg weight attached to one end of a horizontal spring with spring constant 80 N/m. The other end of the spring is anchored to a wall. When a woman working out on the machine pushes her arms forward, a cable stretches the spring by dragging the weight along a track with a coefficient of kinetic friction of 0.30. What is the womans power output at the moment when the weight has moved 50 cm if the cable tension is a constant 100 N?

Upon what basic quantity does kinetic energy depend? Upon what basic quantity does potential energy depend?

Can kinetic energy ever be negative? Can gravitational potential energy ever be negative? For each, give a plausible reason for your answer without making use of any equations

A roller-coaster car rolls down a frictionless track, reaching speed v0 at the bottom. If you want the car to go twice as fast at the bottom, by what factor must you increase the height of the track? Explain.

The three balls in FIGURE Q10.4, which have equal masses, are fired with equal speeds from the same height above the ground. Rank in order, from largest to smallest, their speeds va, vb, and vc as they hit the ground. Explain.

Rank in order, from most to least, the elastic potential energy 1USp2a to 1USp2d stored in the springs of FIGURE Q10.5. Explain.

A spring is compressed 1.0 cm. How far must you compress a spring with twice the spring constant to store the same amount of energy?

A spring gun shoots out a plastic ball at speed v0. The spring is then compressed twice the distance it was on the first shot. By what factor is the balls speed increased? Explain

A particle with the potential energy shown in FIGURE Q10.8 is moving to the right at x = 5 m with total energy E. a. At what value or values of x is this particles speed a maximum?b. Does this particle have a turning point or points in the range of x covered by the graph? If so, where? c. If E is changed appropriately, could the particle remain at rest at any point or points in the range of x covered by the graph? If so, where?

A compressed spring launches a block up an incline. Which objects should be included within the system in order to make an energy analysis as easy as possible?

A process occurs in which a systems potential energy decreases while the system does work on the environment. Does the systems kinetic energy increase, decrease, or stay the same? Or is there not enough information to tell? Explain.

A process occurs in which a systems potential energy increases while the environment does work on the system. Does the systems kinetic energy increase, decrease, or stay the same? Or is there not enough information to tell? Explain.

FIGURE Q10.12 is the energy bar chart for a firefighter sliding down a fire pole from the second floor to the ground. Let the system consist of the firefighter, the pole, and the earth. What are the bar heights of Wext, Kf, and UGf?

a. If the force on a particle at some point in space is zero, must its potential energy also be zero at that point? Explain. b. If the potential energy of a particle at some point in space is zero, must the force on it also be zero at that point? Explain.

Object A is stationary while objects B and C are in motion. Forces from object A do 10 J of work on object B and 5 J of work on object C. Forces from the environment do 4 J of work on object B and 8 J of work on object C. Objects B and C do not interact. What are Ktot and Uint if (a) objects A, B, and C are defined as separate systems and (b) one system is defined to include objects A, B, and C and their interactions?

A system of two objects has Ktot = 7 J and Uint = -5 J. a. How much work is done by interaction forces? b. How much work is done by external forces?

The lowest point in Death Valley is 85 m below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 m. What is the change in potential energy when an energetic 65 kg hiker makes it from the floor of Death Valley to the top of Mt. Whitney?

a. What is the kinetic energy of a 1500 kg car traveling at a speed of 30 m/s (65 mph)? b. From what height would the car have to be dropped to have this same amount of kinetic energy just before impact?

a. With what minimum speed must you toss a 100 g ball straight up to just touch the 10-m-high roof of the gymnasium if you release the ball 1.5 m above the ground? Solve this problem using energy. b. With what speed does the ball hit the ground?

What height does a frictionless playground slide need so that a 35 kg child reaches the bottom at a speed of 4.5 m/s?

A 55 kg skateboarder wants to just make it to the upper edge of a quarter pipe, a track that is one-quarter of a circle with a radius of 3.0 m. What speed does he need at the bottom?

What minimum speed does a 100 g puck need to make it to the top of a 3.0-m-long, 20 frictionless ramp?

A pendulum is made by tying a 500 g ball to a 75-cm-long string. The pendulum is pulled 30 to one side, then released. What is the balls speed at the lowest point of its trajectory?

A 20 kg child is on a swing that hangs from 3.0-m-long chains. What is her maximum speed if she swings out to a 45 angle?

A 1500 kg car traveling at 10 m/s suddenly runs out of gas while approaching the valley shown in FIGURE EX10.11. The alert driver immediately puts the car in neutral so that it will roll. What will be the cars speed as it coasts into the gas station on the other side of the valley?

The maximum energy a bone can absorb without breaking is surprisingly small. Experimental data show that the leg bones of a healthy, 60 kg human can absorb about 200 J. From what maximum height could a 60 kg person jump and land rigidly upright on both feet without breaking his legs? Assume that all energy is absorbed by the leg bones in a rigid landing

A cannon tilted up at a 30 angle fires a cannon ball at 80 m/s from atop a 10-m-high fortress wall. What is the balls impact speed on the ground below?

In a hydroelectric dam, water falls 25 m and then spins a turbine to generate electricity. a. What is UG of 1.0 kg of water? b. Suppose the dam is 80% efficient at converting the waters potential energy to electrical energy. How many kilograms of water must pass through the turbines each second to generate 50 MW of electricity? This is a typical value for a small hydroelectric dam.

How far must you stretch a spring with k = 1000 N/m to store 200 J of energy?

A stretched spring stores 2.0 J of energy. How much energy will be stored if the spring is stretched three times as far?

A student places her 500 g physics book on a frictionless table. She pushes the book against a spring, compressing the spring by 4.0 cm, then releases the book. What is the books speed as it slides away? The spring constant is 1250 N/m

A block sliding along a horizontal frictionless surface with speed v collides with a spring and compresses it by 2.0 cm. What will be the compression if the same block collides with the spring at a speed of 2v?

A 10 kg runaway grocery cart runs into a spring with spring constant 250 N/m and compresses it by 60 cm. What was the speed of the cart just before it hit the spring?

As a 15,000 kg jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it down. The cable is attached to a spring with spring constant 60,000 N/m. If the spring stretches 30 m to stop the plane, what was the planes landing speed?

The elastic energy stored in your tendons can contribute up to 35, of your energy needs when running. Sports scientists find that (on average) the knee extensor tendons in sprinters stretch 41 mm while those of nonathletes stretch only 33 mm. The spring constant of the tendon is the same for both groups, 33 N/mm. What is the difference in maximum stored energy between the sprinters and the nonathletes?

The spring in FIGURE EX10.22a is compressed by x. It launches the block across a frictionless surface with speed v0. The two springs in FIGURE EX10.22b are identical to the spring of Figure EX10.22a. They are compressed by the same x and used to launch the same block. What is the blocks speed now?

The spring in FIGURE EX10.23a is compressed by x. It launches the block across a frictionless surface with speed v0. The two springs in FIGURE EX10.23b are identical to the spring of Figure EX10.23a. They are compressed the same total x and used to launch the same block. What is the blocks speed now?

FIGURE EX10.24 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0 m. a. Will the particle move to the right or to the left? b. What is the particles maximum speed? At what position does it have this speed? c. Where are the turning points of the motion?

FIGURE EX10.25 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particles speeds at B, C, and D?

In FIGURE EX10.26, what is the maximum speed of a 2.0 g particle that oscillates between x = 2.0 mm and x = 8.0 mm?

a. In FIGURE EX10.27, what minimum speed does a 100 g particle need at point A to reach point B? b. What minimum speed does a 100 g particle need at point B to reach point A?

FIGURE EX10.28 shows the potential energy of a 500 g particle as it moves along the x-axis. Suppose the particles mechanical energy is 12 J. a. Where are the particles turning points? b. What is the particles speed when it is at x = 4.0 m? c. What is the particles maximum speed? At what position or positions does this occur? d. Suppose the particles energy is lowered to 4.0 J. Can the particle ever be at x = 2.0 m? At x = 4.0 m?

In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m?

A system in which only one particle can move has the potential energy shown in FIGURE EX10.30. What is the x-component of the force on the particle at x = 5, 15, and 25 cm?

A system in which only one particle can move has the potential energy shown in FIGURE EX10.31. What is the y-component of the force on the particle at y = 0.5 m and 4 m?

A particle moving along the y-axis is in a system with potential energy U = 4y3 J, where y is in m. What is the y-component of the force on the particle at y = 0 m, 1 m, and 2 m?

A particle moving along the x-axis is in a system with potential energy U = 10/x J, where x is in m. What is the x-component of the force on the particle at x = 2 m, 5 m, and 8 m?

FIGURE EX10.34 shows the potential energy of a system in which a particle moves along the x-axis. Draw a graph of the force Fx as a function of position x.

A particle moves from A to D in FIGURE EX10.35 while experiencing force F u = 16ni + 8nj2 N. How much work does the force do if the particle follows path (a) ABD, (b) ACD, and (c) AD? Is this a conservative force? Explain.

A force does work on a 50 g particle as the particle moves along the following straight paths in the xy-plane: 25 J from 10 m, 0 m2 to 15 m, 0 m2; 35 J from 10 m, 0 m2 to 10 m, 5 m2; 5 J from 15 m, 0 m2 to 15 m, 5 m2; 15 J from 10 m, 5 m2 to 15 m, 5 m2; and 20 J from 10 m, 0 m2 to 15 m, 5 m2. a. Is this a conservative force? b. If the zero of potential energy is at the origin, what is the potential energy at 15 m, 5 m2?

A system loses 400 J of potential energy. In the process, it does 400 J of work on the environment and the thermal energy increases by 100 J. Show this process on an energy bar chart

What is the final kinetic energy of the system for the process shown in FIGURE EX10.38?

How much work is done by the environment in the process shown in FIGURE EX10.39? Is energy transferred from the environment to the system or from the system to the environment?

A cable with 20.0 N of tension pulls straight up on a 1.50 kg block that is initially at rest. What is the blocks speed after being lifted 2.00 m? Solve this problem using work and energy

A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The ice cubes speed at the bottom of the circle is 3.0 m/s. What is the ice cubes speed at the top?

A 50 g ice cube can slide up and down a frictionless 30 slope. At the bottom, a spring with spring constant 25 N/m is compressed 10 cm and used to launch the ice cube up the slope. How high does it go above its starting point?

You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 10-m-high hill, then descends 15 m to the tracks lowest point. Youve determined that the spring can be compressed a maximum of 2.0 m and that a loaded car will have a maximum mass of 400 kg. For safety reasons, the spring constant should be 10% larger than the minimum needed for the car to just make it over the top. a. What spring constant should you specify? b. What is the maximum speed of a 350 kg car if the spring is compressed the full amount?

Its been a great day of new, frictionless snow. Julie starts at the top of the 60 slope shown in FIGURE P10.44. At the bottom, a circular arc carries her through a 90 turn, and she then launches off a 3.0-m-high ramp. How far horizontally is her touchdown point from the end of the ramp?

A block of mass m slides down a frictionless track, then around the inside of a circular loop-the-loop of radius R. From what minimum height h must the block start to make it around without falling off? Give your answer as a multiple of R.

A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 50 cm. What is the spring constant of the spring?

You have a ball of unknown mass, a spring with spring constant 950 N/m, and a meter stick. You use various compressions of the spring to launch the ball vertically, then use the meter stick to measure the balls maximum height above the launch point. Your data are as follows: Compression (cm) Height (cm) 2.0 32 3.0 65 4.0 115 5.0 189 Use an appropriate graph of the data to determine the balls mass

Sam, whose mass is 75 kg, straps on his skis and starts down a 50-m-high, 20 frictionless slope. A strong headwind exerts a horizontal force of 200 N on him as he skies. Use work and energy to find Sams speed at the bottom.

A horizontal spring with spring constant 100 N/m is compressed 20 cm and used to launch a 2.5 kg box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Use work and energy to find how far the box slides across the rough surface before stopping.

Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling resistance as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.40. Use work and energy to find the length of a ramp that will stop a 15,000 kg truck that enters the ramp at 35 m/s (75 mph).

A freight company uses a compressed spring to shoot 2.0 kg packages up a 1.0-m-high frictionless ramp into a truck, as FIGURE P10.51 shows. The spring constant is 500 N/m and the spring is compressed 30 cm. a. What is the speed of the package when it reaches the truck? b. A careless worker spills his soda on the ramp. This creates a 50-cm-long sticky spot with a coefficient of kinetic friction 0.30. Will the next package make it into the truck?

Use work and energy to find an expression for the speed of the block in FIGURE P10.52 just before it hits the floor if (a) the coefficient of kinetic friction for the block on the table is mk and (b) the table is frictionless

a. A 50 g ice cube can slide without friction up and down a 30 slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10 cm. The spring constant is 25 N/m. When the ice cube is released, what total distance will it travel up the slope before reversing direction? b. The ice cube is replaced by a 50 g plastic cube whose coefficient of kinetic friction is 0.20. How far will the plastic cube travel up the slope? Use work and energy

The spring shown in FIGURE P10.54 is compressed 50 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The students coefficient of kinetic friction on the 30 incline is 0.15. a. What is the students speed just after losing contact with the spring? b. How far up the incline does the student go?

Protons and neutrons (together called nucleons) are held together in the nucleus of an atom by a force called the strong force. At very small separations, the strong force between two nucleons is larger than the repulsive electrical force between two protonshence its name. But the strong force quickly weakens as the distance between the protons increases. A well-established model for the potential energy of two nucleons interacting via the strong force is U = U0 31 - e-x/x0 4 where x is the distance between the centers of the two nucleons, x0 is a constant having the value x0 = 2.0 * 10-15 m, and U0 = 6.0 * 10-11 J. Quantum effects are essential for a proper understanding of nucleons, but let us innocently consider two neutrons as if they were small, hard, electrically neutral spheres of mass 1.67 * 10-27 kg and diameter 1.0 * 10-15 m. Suppose you hold two neutrons 5.0 * 10-15 m apart, measured between their centers, then release them. What is the speed of each neutron as they crash together? Keep in mind that both neutrons are moving

A 2.6 kg block is attached to a horizontal rope that exerts a variable force Fx = 120 - 5x2 N, where x is in m. The coefficient of kinetic friction between the block and the floor is 0.25. Initially the block is at rest at x = 0 m. What is the blocks speed when it has been pulled to x = 4.0 m?

A system has potential energy U1x2 = x + sin112 rad/m2x2 as a particle moves over the range 0 m x p m. a. Where are the equilibrium positions in this range? b. For each, is it a point of stable or unstable equilibrium?

A particle that can move along the x-axis is part of a system with potential energy U1x2 = A x2 - B x where A and B are positive constants. a. Where are the particles equilibrium positions? b. For each, is it a point of stable or unstable equilibrium?

A 100 g particle experiences the one-dimensional, conservative force Fx shown in FIGURE P10.59.a. Let the zero of potential energy be at x = 0 m. What is the potential energy at x = 1.0, 2.0, 3.0, and 4.0 m? Hint: Use the definition of potential energy and the geometric interpretation of work. b. Suppose the particle is shot to the right from x = 1.0 m with a speed of 25 m/s. Where is its turning point

A clever engineer designs a sprong that obeys the force law Fx = -q1x - xeq23 , where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, well let xeq = 0 m. Then Fx = -qx3 .a. What are the units of q? b. Find an expression for the potential energy of a stretched or compressed sprong. c. A sprong-loaded toy gun shoots a 20 g plastic ball. What is the launch speed if the sprong constant is 40,000, with the units you found in part a, and the sprong is compressed 10 cm? Assume the barrel is frictionless.

The potential energy for a particle that can move along the x-axis is U = Ax2 + Bsin1px/L2, where A, B, and L are constants. What is the force on the particle at (a) x = 0, (b) x = L/2, and (c) x = L?

A particle that can move along the x-axis experiences an interaction force Fx = 13x2 - 5x2 N, where x is in m. Find an expression for the systems potential energy

An object moving in the xy-plane is subjected to the force F u = 12xy ni + x2 nj2 N, where x and y are in m. a. The particle moves from the origin to the point with coordinates 1a, b2 by moving first along the x-axis to 1a, 02, then parallel to the y-axis. How much work does the force do? b. The particle moves from the origin to the point with coordinates 1a, b2 by moving first along the y-axis to 10, b2, then parallel to the x-axis. How much work does the force do? c. Is this a conservative force?

An object moving in the xy-plane is subjected to the force F u = 12xyni + 3ynj2 N, where x and y are in m. a. The particle moves from the origin to the point with coordinates 1a, b2 by moving first along the x-axis to 1a, 02, then parallel to the y-axis. How much work does the force do? b. The particle moves from the origin to the point with coordinates 1a, b2 by moving first along the y-axis to 10, b2, then parallel to the x-axis. How much work does the force do? c. Is this a conservative force?

Write a realistic problem for which the energy bar chart shown in FIGURE P10.65 correctly shows the energy at the beginning and end of the problem.

In Problems 66 through 68 you are given the equation used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. b. Draw the before-and-after pictorial representation. c. Finish the solution of the problem.1 2 11500 kg215.0 m/s22 + 11500 kg219.80 m/s2 2110 m2 = 1 2 11500 kg2vi 2 + 11500 kg219.80 m/s2 210 m2

In Problems 66 through 68 you are given the equation used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. b. Draw the before-and-after pictorial representation. c. Finish the solution of the problem.2 10.20 kg212.0 m/s22 + 1 2 k10 m22 = 1 2 10.20 kg210 m/s22 + 1 2 k1-0.15 m22

In Problems 66 through 68 you are given the equation used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. b. Draw the before-and-after pictorial representation. c. Finish the solution of the problem.2 10.50 kg2vf 2 + 10.50 kg219.80 m/s2 210 m2 + 1 2 1400 N/m210 m22 = 1 2 10.50 kg210 m/s22 + 10.50 kg219.80 m/s2 211-0.10 m2 sin 302 + 1 2 1400 N/m21-0.10 m2

A pendulum is formed from a small ball of mass m on a string of length L. As FIGURE CP10.69 shows, a peg is height h = L/3 above the pendulums lowest point. From what minimum angle u must the pendulum be released in order for the ball to go over the top of the peg without the string going slack?

In a physics lab experiment, a compressed spring launches a 20 g metal ball at a 30 angle. Compressing the spring 20 cm causes the ball to hit the floor 1.5 m below the point at which it leaves the spring after traveling 5.0 m horizontally. What is the spring constant?

Its your birthday, and to celebrate youre going to make your first bungee jump. You stand on a bridge 100 m above a raging river and attach a 30-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 40 N/m. Assume that your mass is 80 kg. After a long hesitation, you dive off the bridge. How far are you above the water when the cord reaches its maximum elongation?

A 10 kg box slides 4.0 m down the frictionless ramp shown in FIGURE CP10.72, then collides with a spring whose spring constant is 250 N/m. a. What is the maximum compression of the spring? b. At what compression of the spring does the box have its maximum speed?

The spring in FIGURE CP10.73 has a spring constant of 1000 N/m. It is compressed 15 cm, then launches a 200 g block. The horizontal surface is frictionless, but the blocks coefficient of kinetic friction on the incline is 0.20. What distance d does the block sail through the air?

A sled starts from rest at the top of the frictionless, hemispherical, snow-covered hill shown in FIGURE CP10.74. a. Find an expression for the sleds speed when it is at angle f. b. Use Newtons laws to find the maximum speed the sled can have at angle f without leaving the surface. c. At what angle fmax does the sled fly off the hill?