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A sphere of mass m = 2.5 kg can move across a horizontal, frictionless surface. Attached to the sphere is an ideal spring with spring constant k = 27 N/m. At time t = 0 the sphere is pulled aside from the equilibrium position, x=0, a distance d = 12 cm in the positive direction and released from rest. After this time, the system oscillates between x = ± d.

Determine the magnitude of the force, in newtons, required to initially displace the sphere d=11 cm from equilibrium

Respuesta :

Answer:

F = 2.97 N

Explanation:

Since the surface is frictionless, the mass of the sphere has no effect on the force required to pull the sphere. The force that the spring applies is as follows

[tex]\vec{F} = -k\vec{x}[/tex]

Therefore, the magnitude of the force required to initially displace the sphere d = 11 cm is

[tex]F = 27(0.11) = 2.97~N[/tex]

The magnitude of the force that will be needed in order to displace the sphere from equilibrium will be 2.97 Newton.

Based on the information given, it can be deduced that the sphere will have no effect on the force that's required to pull the sphere due to the fact that the surface is frictionless.

Therefore, the formula for the force will be:

F = kx

F = 27(0.11) = 2.97 Newton.

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