A particle moves through an xyz coordinate system

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4. A particle moves through an xyz coordinate system while a force acts on the particle. When the particle has the position vector ~ r = (2 m ) ˆ i - (3 m ) ˆ j +(2 m ) ˆ k , the force is ~ F = F x ˆ i +(7 N ) ˆ j - (6 N ) ˆ k , and the corresponding torque about the origin is ~ τ = (4 N · m ) ˆ i + (2 N · m ) ˆ j - (1 N · m ) ˆ k . What is the x-component of the force, F x ? (1) - 5 N (2) 5 N (3) - 10 N (4) 10 N (5) - 1 N 5. A single force acts on a particle located on the positive x axis a distance d from the origin (i.e. at the point P = (x,y,z) = (d,0,0)). The torque about the origin is non-zero and points in the negative y direction. The force must be: (1) in the positive z direction(2) in the negative z direction(3) in the positive x direction(4) in the negative x direction (5) in the positive y direction 6. A 0.5-kg particle moves along the x axis under the influence of a conservative force. The potential energy is given by U ( x ) = (8 J/m 2 ) x 2 + (2 J/m 4 ) x 4 , where x is the coordinate of the particle in meters. If the particle has a speed of 5 m/s when it is at x = 1 m, its speed when it is at the origin is: (1) 8.1 m/s (2) 0 m/s (3) 5.0 m/s (4) 6.3 m/s (5) 65 m/s 7. A particle moves along the x-axis under the influence of a conservative force. The potential energy is given by U ( x ) = (3 J/m 2 ) x 2 - (12 J/m ) x + 12 J , where the particle. If the total mechanical energy is 12 J, the limits of motion are: (1) 0 m; 4 m (2) 0 m; 2 m (3) - 4 m; 4 m (4) - 4 m; 0 m (5) - 2 m; 0 m 8. A particle moves along the x-axis under the influence of a conservative force. The potential energy is given by U ( x ) = (3 J/m 2 ) x 2 - (12 J/m ) x , where the particle. At what value of the position x is the force on the particle equal to zero? (1) x = 2 m (2) x = 4 m (3) x = 6 m (4) x = 0 (5) The force is not zero at any value of x
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77777 77777 9. The figure shows a cubical box with each side consisting of a uniform metal plate of negligible thickness. Each of the four sides have mass, M , and the bottom has mass 2 M . The box is open at the top (at z = L ) and has edge length L . What is the z -coordinate of the center-of-mass?
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