The graph above shows the potential energy of an object that moves without the influence of other forces. The object has a mass of m = 0.46 kg. At one time the object is at the location x = 2.0 meters. What speed does the object need to have at the location x = 2.0 meters in order to escape from the potential well? [This is the same as asking for the escape velocity of the object at that point.] Answer in units of meters/second.

In the figure below an object of mass m starts from rest on a roller coaster with negligible friction. A hA B hB C hc Ꭰ hp (a) What terms are present in the object's mechanical energy? Choose from E O Gravitational potential energy, Spring potential energy, Kinetic energy, Work done against friction O Gravitational potential energy, Spring potential energy, Kinetic energy Spring potential energy, Kinetic energy, Work done against friction, Gravitational potential energy, Kinetic energy because, there is no friction (b) Mechanical energy is conserved Only conservative forces ◆ act. (c) Calculate the speed of the object at point D (VD) in terms of the following variables: (g, ha, hD)

A block of mass 3 kg compresses spring 1 with a force constant, k1=7000 N/m, by 6 cm. It is released and slides for a total of 50 cm on a surface with μk=0.2, at which point it compresses another spring 2, k2=1000 N/m, and momentarily comes to rest. Remember that Us is the potential energy of the spring. Find the following values:What is the Initial spring potential energy of spring 1? How much energy is dissipated by heat? This is the amount of work done by friction × -1. How much Potential Energy does spring 2 have when the block has compressed spring 2 and is momentarily stopped? By how much does spring 2 compress?

A conservative force F is in +x-direction and has a magnitude F(x)=3.00/(x+0.080)4 N. Let U(x) approach 0 when x approaches infinity. An object with mass 5.00 kg is released from rest at x = 0 and moves in the +x-direction. If F is the only force action on the object, what is the object's speed when it reaches x = 0.500 m?

A particle of mass 18.8 kg moves along the x-axis with a potential energy U whose dependence on position x is shown in the figure. If the total mechanical energy E of the particle is 110 J, what is the speed in m/s of the particle at 7 m? 15 U (J) 10 V. 5 4 8 10 X (m) 00 6. 20

The figure here shows a plot of potential energy U versus position x of a 0.888 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) Three values are Ug = 15.0 J, Ug = 35.0 J and Uc = 45.0 J. The particle is released at x = 4.50 m with an initial speed of 7.04 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (b) magnitude and (c) direction of the force on the particle as it begins to move to the left of x = 4.00 m? Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.50 m at speed 7.04 m/s. (d) If the particle can reach x = 7.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (e) magnitude and (f) direction of the force on the particle as it begins to move to the right of x = 5.00 m? Uc UB UA 4 6 x (m) (a) Number Unit (b) Number Unit (c) (d) Number…

The figure here shows a plot of potential energy U versus position x of a 0.878 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) Three values are U = 15.0 J, Ug = 35.0 J and Uc 45.0 J. The particle is released at x = 4.50 m with an initial speed of 7.70 m/s, headed in the negative x direction. (a) If the particle can reach x 1.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (b) magnitude and (c) direction of the force on the particle as it begins to move to the left of x = 4.00 m? Suppose, instead, the particle is headed in the positive x direction when it is released at x 4.50 m at speed 7.70 m/s. (d) If the particle can reach x 7.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (e) magnitude and (f) direction of the force on the particle as it begins to move to the right of x 5.00 m? UB UA 6 (m) Unit (a) Number (b) Number Unit (c) (d) Number |Unit (e) Number…

A single conservative force acts on a 4.70-kg particle within a system due to its interaction with the rest of the system. The equation Fx = 2x + 4 describes the force, where Fx is in newtons and x is in meters. As the particle moves along the x axis from x = 0.96 m to x = 7.50 m, calculate the following. (a) the work done by this force on the particle 81.488 J (b) the change in the potential energy of the system J (c) the kinetic energy the particle has at x = 7.50 m if its speed is 3.00 m/s at x = 0.96 m J

The figure here shows a plot of potential energy U versus position x of a 6-kg particle that can travel only along an x axis. Nonconservative forces are not involved. When the particle is at x = 1 m, it is moving in the +x direction with a kinetic energy of 100 J. Potential Energy Versus x Potential Energy U(U) 100 20 0 1 2 3 7 Position x (m) 4 5 6 8 9 10 11 12 a. What is the acceleration of the particle at x = 3.5 m? Include a plus or minus sign to indicate direction.

The figure below shows a plot of potential energy U versus position x of a 0.76 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) In the graphs, the potential energies are UA = 20.0 J, UB = 35.0 J, and Uc = 45.0 J. Uc UB UA 4 х (m) The particle is released at x = 4.5 m with an initial speed of 6.0 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.0 m, what is its speed there, and if it cannot, what is its turning point? m (b) What are the magnitude and direction of the force on the particle as it begins to move to the left of x = 4.0 m? magnitude direction +X Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.5 m at speed 6.0 m/s. (c) If the particle can reach x = 7.0 m, what is its speed there, and if it cannot, what is its turning point? m (d) What are the magnitude and direction of the force on the particle as it begins to move to the right of x = 5.0 m? magnitude…