Question

05.3 Consider a spring that does not obey Hooke's law very faithfully. One end of the spring is fixed. To keep the spring stretched or compressed an amount x, a force along the x-axis with xcomponent Fx =kx – bx2 + cx3 must be applied to the free end, where k = 130 N/m, b = 660 N/m2 , and c = 16000 N/m3 . Note that x > 0 when the spring is stretched and x < 0 when it is compressed. (Many real springs behave in a similar fashion.)

(a) How much work must be done to stretch this spring by 0.050 m from its unstretched length?

(b) How much work must be done to compress this spring by 0.050 m from its unstretched length?

(c) How much work must be done to move the spring from being compressed by 0.070 m to being stretched by 0.030 m, assuming the end moves with constant speed during the motion?

Answer #1

A light spring obeys Hooke's law. The spring's unstretched
length is 31.5 cm. One end of the spring is attached to the top of
a doorframe and a weight with mass 8.00 kg is hung from the other
end. The final length of the spring is 43.5 cm.
(a)
Find its spring constant (in N/m).
N/m
(b)
The weight and the spring are taken down. Two people pull in
opposite directions on the ends of the spring, each with a...

Hooke's law describes a certain light spring of unstretched
length 38.0 cm. When one end is attached to the top of a door frame
and a 6.00-kg object is hung from the other end, the length of the
spring is 42.5 cm.
(a) Find its spring constant.
_________ kN/m
(b) The load and the spring are taken down. Two people pull in
opposite directions on the ends of the spring, each with a force of
180 N. Find the length...

1. Hook's law describes an ideal spring. Many real springs are
better described by the restoring force (FSp)s=−kΔs−q(Δs)3, where q
is a constant. Consider a spring with k = 200 N/m and q = 750
N/m3.
Part A: How much work must you do to compress this spring 15 cm?
Note that, by Newton's third law, the work you do on the spring is
the negative of the work done by the spring. Express your answer
with the appropriate units....

According to Hooke’s Law, the force required to maintain
a spring stretched x units beyond its natural length is
proportional to x, that is,fx=k x. A force of 40 N is required to
hold a spring that has been stretched from its natural length of 10
cm to a length of 15 cm. How much work is done in stretching the
spring from 15 cm to 18 cm?
Item 3a Below, show all work to set up the integral that...

A 2.5-kg block is sliding along a rough horizontal surface and
collides with a horizontal spring whose spring constant is 320 N/m.
Unstretched, the spring is 20.0 cm long. The block causes the
spring to compress to a length of 12.5 cm as the block temporarily
comes to rest. The coefficient of kinetic friction between the
block and the horizontal surface is 0.25. a) How much work is done
by the spring as it brings the block to rest? b)...

A pen contains a spring with a spring constant of 275 N/m. When
the tip of the pen is in its retracted position, the spring is
compressed 5.6 mm from its unstrained length. In order to push the
tip out and lock it into its writing position, the spring must be
compressed an additional 6.7 mm. How much work is done by the
spring force to ready the pen for writing? Be sure to include the
proper algebraic sign with...

A pen contains a spring with a spring constant of 292 N/m. When
the tip of the pen is in its retracted position, the spring is
compressed 4.40 mm from its unstrained length. In order to push the
tip out and lock it into its writing position, the spring must be
compressed an additional 6.00 mm. How much work is done by the
spring force to ready the pen for writing? Be sure to include the
proper algebraic sign with...

A pen contains a spring with a spring constant of 204 N/m. When
the tip of the pen is in its retracted position, the spring is
compressed 5.40 mm from its unstrained length. In order to push the
tip out and lock it into its writing position, the spring must be
compressed an additional 5.10 mm. How much work is done by the
spring force to ready the pen for writing? Be sure to include the
proper algebraic sign with...

A block with mass m = 14 kg rests on a frictionless table and is
accelerated by a spring with spring constant k = 4399 N/m after
being compressed a distance x1 = 0.468 m from the
spring’s unstretched length. The floor is frictionless except for a
rough patch a distance d = 2 m long. For this rough path, the
coefficient of friction is μk = 0.48.
1)How much work is done by the spring as it accelerates the...

1. A 150 g particle at x = 0 is moving at 2.00 m/s in the
+x-direction. As it moves, it experiences a force given by
Fx=(0.750N)sin(x/2.00m).
Part A: What is the particles speed when it reaches x = 3.14 m?
Express your answer with the appropriate units.
2. Hook's law describes an ideal spring. Many real springs are
better described by the restoring force (FSp)s=−kΔs−q(Δs)3, where q
is a constant. Consider a spring with k = 200 N/m and...

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