Step 4: Calculate the distance the spring is compressed The distance the spring is compressed can be calculated using the formula for the potential energy stored in a spring: PE = kx where k is the spring constant (3000 N/m) and x is the distance the spring is compressed. Setting this equal to the kinetic energy of the package and solving for x, we get: 28.84 J = 3000 N/mxx 2 Solving for x, we get: x = 2x28.84 J 3000 N/m = 0.49 m Step 5: Determine if the package will stop before it gets back to the ramp The package will stop before it gets back to the ramp if the work done by friction as it is pushed back by the spring is greater than the kinetic energy it has when it is released by the spring. The work done by friction can be calculated as before, but with the distance being the distance the package travels before it stops. This distance is equal to the distance the spring was compressed plus the distance to the ramp, or 0.49 m + 12 m = 12.49 m. Substituting these values into the formula for work, we get: W = 0.21 × 2 kg × 9.8 m/s² × 12.49 m = 51.6 J Since this is greater than the kinetic energy of the package when it is released by the spring (28.84 J), the package will stop before it gets back to the ramp. Solution The package compresses the spring a distance of 0.49 m before coming momentarily to rest. The package will stop before it gets back to the ramp.
Step 4: Calculate the distance the spring is compressed The distance the spring is compressed can be calculated using the formula for the potential energy stored in a spring: PE = kx where k is the spring constant (3000 N/m) and x is the distance the spring is compressed. Setting this equal to the kinetic energy of the package and solving for x, we get: 28.84 J = 3000 N/mxx 2 Solving for x, we get: x = 2x28.84 J 3000 N/m = 0.49 m Step 5: Determine if the package will stop before it gets back to the ramp The package will stop before it gets back to the ramp if the work done by friction as it is pushed back by the spring is greater than the kinetic energy it has when it is released by the spring. The work done by friction can be calculated as before, but with the distance being the distance the package travels before it stops. This distance is equal to the distance the spring was compressed plus the distance to the ramp, or 0.49 m + 12 m = 12.49 m. Substituting these values into the formula for work, we get: W = 0.21 × 2 kg × 9.8 m/s² × 12.49 m = 51.6 J Since this is greater than the kinetic energy of the package when it is released by the spring (28.84 J), the package will stop before it gets back to the ramp. Solution The package compresses the spring a distance of 0.49 m before coming momentarily to rest. The package will stop before it gets back to the ramp.
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Step 4: Calculate the distance the spring is compressed
The distance the spring is compressed can be calculated using the formula for the potential energy stored in
a spring:
PE =
kx
where k is the spring constant (3000 N/m) and x is the distance the spring is compressed. Setting this equal
to the kinetic energy of the package and solving for x, we get:
28.84 J =
3000 N/mxx
2
Solving for x, we get:
x =
2x28.84 J
3000 N/m
= 0.49 m
Step 5: Determine if the package will stop before it gets back to the ramp
The package will stop before it gets back to the ramp if the work done by friction as it is pushed back by the
spring is greater than the kinetic energy it has when it is released by the spring. The work done by friction
can be calculated as before, but with the distance being the distance the package travels before it stops.
This distance is equal to the distance the spring was compressed plus the distance to the ramp, or 0.49 m +
12 m = 12.49 m. Substituting these values into the formula for work, we get:
W = 0.21 × 2 kg × 9.8 m/s² × 12.49 m = 51.6 J
Since this is greater than the kinetic energy of the package when it is released by the spring (28.84 J), the
package will stop before it gets back to the ramp.
Solution
The package compresses the spring a distance of 0.49 m before coming momentarily to rest. The package
will stop before it gets back to the ramp.
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