The block in the figure lies on a horizontal frictionless surface, and the sprin

Question

The block in the figure lies on a horizontal frictionless surface, and the spring constant is 46 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 4.0 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. When that stopping point is reached, what are (a) the position of the block, (b) the work that has been done on the block by the applied force, and (c) the work that has been done on the block by the spring force? During the block's displacement, what are (d) the block's position when its kinetic energy is maximum and (e) the value of that maximum kinetic energy?

The block in the figure lies on a horizontal frictionless surface, and the spring constant is 46 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 4.0 N pulls the block in the positive direction of the x axis, stretching the spring until the block stops. When that stopping point is reached, what are (a) the position of the block, (b) the work that has been done on the block by the applied force, and (c) the work that has been done on the block by the spring force? During the block's displacement, what are (d) the block's position when its kinetic energy is maximum and (e) the value of that maximum kinetic energy?

Explanation / Answer

let x be extension

spring constant k = 46 N/m

F= 4.0 N

(a) Work done by force = final potential energy of spring
Fx = (1/2)kx2

x = 2*F/k

= 2*4/46

= 0.174 m

(b) work done on the block by applied force = (1/2)kx2

= 0.5 * 46 * 0.1742

= 0.6964 J

(c) work done on the block by spring = - (work done on the block by applied force)

= - 0.6964 J

(d)  block's position when its kinetic energy is maximum, x = F / k

= 4/46

= 0.087 m

(e) Maximum KE = U at max stretch x = (1/2)kx2

= 0.5*46*0.0872   

= 0.1741 J

= 174.1 mJ

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