The figure gives the one-dimensional potential energy well for a 1.80 kg particle (the function U(x) has the form bx2 and the vertical axis scale is set by Ug = 2.0 J).(a) If the particle passes through the equilibrium position with a velocity of 50.0 cm/s, will it be turned back before it reaches x = 16.0 cm?(b) If yes, at what position, and if no, what is the speed of the particle at x = 16.0 cm? U (J) -20 -10 10 20 x (cm) (a) Yes (b) Number Units cm

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A particle can move along only an x axis, where conservative forces act on it (see the figure and the table below). The particle is released at x = 5.00 m with a kinetic energy of K = 14.0 J and a potential energy of U = 0.0 J. If its motion is in the negative direction of the x axis, what are its (a) K and (b) U at x = 2.00 m and its (c) K and (d) U at x = 0? If its motion is in the positive direction of the x axis, what are its (e) K and (f) U at x = 11.0 m, its (g) K and (h) U at x = 12.0 m, and its (i) K and (j) U at x = 13.0 m? Next, the particle is released from rest at x = 0. What are (k) its kinetic energy at x = 5.0 m and (I) the maximum positive position xmax it reaches? F, x (m) 4 6. 8 10 12 Range Force F = +(3.00 N)i F, = +(5.00 N)i O to 2.00 m 2.00 m to 3.00 m 3.00 m to 8.00 m F = 0 F, = -(4.00 N)i F, = -(1.00 N)i 8.00 m to 11.0 m 11.0 m to 12.0 m 12.0 m to 15.0 m F = 0

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…

In the figure, a spring with spring constant k = 180 N/m is at the top of a frictionless incline of angle e = 38°. The lower end of the incline is distance D = 0.92 m from the end of the spring, which is at its relaxed length. A 1.5 kg canister is pushed against the spring until the spring is compressed 0.22 m and released from rest. (a) What is the speed of the canister at the instant the spring returns to its relaxed length (which is when the canister loses contact with the spring)? (b) What is the speed of the canister when it reaches the lower end of the incline? (a) Number UnitšTm/s (b) Number Unitsm/s Click if you would like to Show Work for this question: Open Show Work Question Attempts: Unlimited SAVE FOR LATER SUBMIT ANSWER 10:37 PM ENG e to search 4/4/2021 13) 19home & 7. LEGO 08. 9. E R. Y

A single conservative force F = (7.0x - 11)§ N, where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 27 J at x = 0. (a) What is the maximum positive potential energy? At what (b) negative value and (c) positive value of x is the potential energy equal to zero?

A conservative force F(x) acts on a 1.8 kg particle that moves along an x axis. The potential energy U(x) associated with F(x) is graphed in the figure. When the particle is at x = 2.0 m, its velocity is - 1.5 m/s. (a) What is F(x) at this position, including sign? Between what positions on the (b) left and (c) right does the particle move? (d) What is its particle's speed at x = 7.0 m? x (m) 5 10 15 -5 -10 -15 -20 (a) Number 4.7 Units Units (b) Number i -5.0 Units i 14 (c) Number Units m/s i 3.7 (d) Number (() (* )1

A particle moves along a curved path y(x) = (10 m){1+cos[(0.1 m−1)x]} , from x = 0 to x = 10π m, subject to a tangential force of variable magnitude F(x) = (10 N)sin[(0.1 m−1)x]. How much work does the force do? (Hint: Consult a table of integrals or use a numerical integration program.)

The figure here shows a plot of potential energy U versus position x of a 0.876 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) Three values are UA = 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 7.96 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 7.96 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? UcT UB 4 x (m) (a) Number i Unit (b) Number i Unit (c) (d) Number i…

A particle moves along the x-axis while acted on by a single conservative force parallel to the x-axis. The force corresponds to the potential-energy function graphed in the Figure. U (J) 4.0 C 2.0 +x (m) 0,5 1.5 2.0 2.5 B -2.0 The particle is released from rest at point A. (a) What is the direction of the force on the particle when it is at point 4? (b) At point B? (c) At what value of x is the kinetic energy of the particle a maximum? (d) What is the force on the particle when it is at point C? (e) What is the largest value of x reached by the particle during its motion? (f) What value or values of x correspond to points of stable equilibrium? (g) Of unstable equilibrium?