18. A frictionless inclined plane forms angle 0 = 20° with the horizontal as shown in the figure. A spring with force constant k = 500 N/m is fastened securely at the bottom of the incline so that the spring is parallel to the surface. A block of mass m = 2.5 kg is placed on the incline at a distance d = 0.3 m from the spring. From this position, the block is projected toward the spring with initial speed v = 0.750 m/s. After making contact with the spring, the block gradually slows down as it compresses the spring. Calculate the maximum compression of the spring. ww.

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18. A frictionless inclined plane forms angle 0 = 20°
with the horizontal as shown in the figure. A
spring with force constant k = 500 N/m is
fastened securely at the bottom of the incline so
that the spring is parallel to the surface. A block
of mass m = 2.5 kg is placed on the incline at a
distance d = 0.3 m from the spring. From this
position, the block is projected toward the spring
with initial speed v = 0.750 m/s. After making
contact with the spring, the block gradually slows
down as it compresses the spring. Calculate the maximum compression of the spring.
Hint: There are several ways to solve this challenging problem. One method is to use
the work-energy theorem: Wnet = AK = Wgrav + Wspring
maximum compression. Then, gravity acts over distance d + x, while the spring force
m
= AK. Let x denote the
acts over distance x.
Transcribed Image Text:18. A frictionless inclined plane forms angle 0 = 20° with the horizontal as shown in the figure. A spring with force constant k = 500 N/m is fastened securely at the bottom of the incline so that the spring is parallel to the surface. A block of mass m = 2.5 kg is placed on the incline at a distance d = 0.3 m from the spring. From this position, the block is projected toward the spring with initial speed v = 0.750 m/s. After making contact with the spring, the block gradually slows down as it compresses the spring. Calculate the maximum compression of the spring. Hint: There are several ways to solve this challenging problem. One method is to use the work-energy theorem: Wnet = AK = Wgrav + Wspring maximum compression. Then, gravity acts over distance d + x, while the spring force m = AK. Let x denote the acts over distance x.
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