Ch 10: Interactions and Potential Energy
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Problem 10
FIGURE EX10.28 shows the potential-energy diagram for a 500 g particle as it moves along the x-axis. Suppose the particle's mechanical energy is 12 J. (a) Where are the particle's turning points?
Problem 10
A system consists of interacting objects A and B, each exerting a constant 3.0 N pull on the other. What is (delta)U for the system if A moves 1.0 m toward B while B moves 2.0 m toward A?Problem 10
A system has potential energy U(x)=(10 J)[1−sin((3.14 rad/m) x)] as a particle moves over the range 0 m≤x≤3 m b. For each, is it a point of stable or unstable equilibrium?Problem 10
CALC A particle that can move along the x -axis is part of a system with potential energy U(x)= A/x2 − B/x where A and B are positive constants. a. Where are the particle's equilibrium positions?Problem 10
A particle moving along the y-axis is in a system with potential energy U = 4y^3 J, where y is in m. What is the -component of the force on the particle at y = 0 m, 1 m, and 2 m?Problem 10
CALC A clever engineer designs a 'sprong' that obeys the force law Fx=−q(x−xeq)³ , where xeq is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we'll let xeq=0 m .Then Fx=−qx³. b. Find an expression for the potential energy of a stretched or compressed sprong.Problem 10
FIGURE EX10.24 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particle's speeds at B, C, and D?
Problem 10
FIGURE EX10.25 is the potential-energy diagram for a 20 g particle that is released from rest at x = 1.0m. (b) What is the particle's maximum speed? At what position does it have this speed?
Problem 10
A stretched spring stores 2.0 J of energy. How much energy will be stored if the spring is stretched three times as far?Problem 10
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.Problem 10
A 50 g mass is attached to a light, rigid, 75-cm-long rod. The other end of the rod is pivoted so that the mass can rotate in a vertical circle. What speed does the mass need at the bottom of the circle to barely make it over the top of the circle?Problem 10
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.Problem 10
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?Problem 10
Two blocks with masses mA and mB are connected by a massless string over a massless, frictionless pulley. Block B, which is more massive than block A, is released from height h and falls. a. Write an expression for the speed of the blocks just as block B reaches the ground.Problem 10
Two blocks with masses mA and mB are connected by a massless string over a massless, frictionless pulley. Block B, which is more massive than block A, is released from height h and falls. b. A 1.0 kg block and a 2.0 kg block are connected by a massless string over a massless, frictionless pulley. The impact speed of the heavier block, after falling, is 1.8 m/s. From how high did it fall?Problem 10
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 student's coefficient of kinetic friction on the 30° incline is 0.15. a. What is the student's speed just after losing contact with the spring?
Problem 10
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?
Problem 10
A system in which only one particle moves has the potential energy shown in FIGURE EX10.31. What is the x-component of the force on the particle at x = 5, 15, and 25 cm?
Problem 10
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 P10.52 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?Problem 10
CALC A 10 kg box slides 4.0 m down the frictionless ramp shown in FIGURE CP10.73, then collides with a spring whose spring constant is 250 N/m. a. What is the maximum compression of the spring?Problem 10
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?Problem 10
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.Problem 10
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 plane's landing speed?Problem 10
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 track's lowest point. You've 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. What is the maximum speed of a 350 kg car if the spring is compressed the full amount?Problem 10
FIGURE 10.23 showed the potential-energy curve for the O2 molecule. Consider a molecule with the energy E1 shown in the figure. a. What is the maximum speed of an oxygen atom as it oscillates back and forth? Don't forget that the kinetic energy is the total kinetic energy of the system. The mass of an oxygen atom is 16 u, where 1 u=1 atomic mass unit =1.66×10(to the poer of)−27 kg .Problem 10
A 1.0 kg mass that can move along the x -axis experiences the potential energy U=(x²−x) J, where x is in m. The mass has velocity v𝓍=3.0 m/s at position x=1.0 m . At what position has it slowed to 1.0 m/s?Problem 10
CALC The potential energy for a particle that can move along the x -axis is U=Ax²+B sin(πx/L) , 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?Problem 10
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?Problem 10
In FIGURE EX10.27, what is the maximum speed of a 2.0 g particle that oscillates between x = 2.0mm and x = 8.0 mmProblem 10
The spring in FIGURE EX10.21a is compressed by 10 cm. It launches a block across a frictionless surface at 0.50 m/s. The two springs in Figure EX10.21b are identical to the spring of Figure EX10.21a. They are compressed by the same 10 cm and launch the same block. What is the block's speed now?
