Question

Use the following for questions 4 and 5: A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pulls horizontally on ar 18-kg box that is resting on a horizontal floor. The coefficient of static friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45 4. How long is the spring just as the box is ready to move? If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long is the 5. spring?

Answer 1

4.Find the minimum force required to move the box

When the box is just about to move, its acceleration is zero and frictional force acting on the box is static frictional force.

Net Force = 0

Pulling force - frictional force =0

F -F friction

F =「friction

$F=\mu _{s}N$

$F=\mu _{s}mg$

F = 0.65 * 18kg * 9.81m/s

F-1 14.777N

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Now consider the spring

Force ,$F=kx$

$x=\frac{F}{k}$

114.777N 2.5N/cm

ANSWER: ${\color{Red} x=45.91cm}$

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5.

When the box is moving with constant velocity ,its acceleration is zero and frictional force acting is kinetic frictional force.

Net Force = 0

Pulling force - frictional force =0

F -F friction

F =「friction

$F=\mu _{k}N$

$F=\mu _{k}mg$

$F=0.45*18kg*9.81m/s^{2}$

${\color{Red} F=79.461N}$

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Now consider the spring

Force ,$F=kx$

$x=\frac{F}{k}$

79.461N 2.5N/cm

ANSWER: ${\color{Red} x=31.78cm}$

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