You have a new internship, where you are helping to design a new freight yard for the train station in your city. There will be a number of dead-end sidings where single cars can be stored until they are needed. To keep the cars from running off the tracks at the end of the siding, you have designed a combination of two coiled springs as illustrated in the figure below. When a car moves to the right in the figure and strikes the springs, they exert a force to the left on the car to slow it down. k2 ki A single railcar is shown on the rail tracks. To its right, but not connected to it, is a combination of two horizontal, coiled springs - one, labeled k,, is broader and shorter and the other, labeled k,, is narrower and longer. Both the springs are connected to a vertical surface. To tal force (N) 2000- 1500 1000 500 Distance (cm) 60 10 20 30 40 50 Both springs are described by Hooke's law and have spring constants k, = 1,800 N/m and k, = 2,800 N/m. After the first spring compresses by a distance of d = 30.0 cm, the second spring acts with the first to increase the force to the left on the car in the figure. When the spring with spring constant k, compresses by 50.0 cm, the coils of both springs are pressed together, so that the springs can %3D no longer compress. A typical car on the siding has a mass of 7,000 kg. When you present your design to your supervisor, he asks you for the maximum speed (in m/s) that a car can have and be stopped by your device.
You have a new internship, where you are helping to design a new freight yard for the train station in your city. There will be a number of dead-end sidings where single cars can be stored until they are needed. To keep the cars from running off the tracks at the end of the siding, you have designed a combination of two coiled springs as illustrated in the figure below. When a car moves to the right in the figure and strikes the springs, they exert a force to the left on the car to slow it down. k2 ki A single railcar is shown on the rail tracks. To its right, but not connected to it, is a combination of two horizontal, coiled springs - one, labeled k,, is broader and shorter and the other, labeled k,, is narrower and longer. Both the springs are connected to a vertical surface. To tal force (N) 2000- 1500 1000 500 Distance (cm) 60 10 20 30 40 50 Both springs are described by Hooke's law and have spring constants k, = 1,800 N/m and k, = 2,800 N/m. After the first spring compresses by a distance of d = 30.0 cm, the second spring acts with the first to increase the force to the left on the car in the figure. When the spring with spring constant k, compresses by 50.0 cm, the coils of both springs are pressed together, so that the springs can %3D no longer compress. A typical car on the siding has a mass of 7,000 kg. When you present your design to your supervisor, he asks you for the maximum speed (in m/s) that a car can have and be stopped by your device.
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You have a new internship, where you are helping to design a new freight yard for the train station in your city. There will be a number of dead-end sidings where single cars can be stored until they are needed. To keep the cars from running off the tracks at the end of the siding, you have designed a combination of two coiled springs as illustrated in the figure below. When a car moves to the right in the figure and strikes the springs, they exert a force to the left on the car to slow it down. Both springs are described by Hooke's law and have spring constants
k1 = 1,800 N/m
and
k2 = 2,800 N/m.
After the first spring compresses by a distance of
d = 30.0 cm,
the second spring acts with the first to increase the force to the left on the car in the figure. When the spring with spring constant k2 compresses by 50.0 cm, the coils of both springs are pressed together, so that the springs can no longer compress. A typical car on the siding has a mass of 7,000 kg. When you present your design to your supervisor, he asks you for the maximum speed (in m/s) that a car can have and be stopped by your device.
Transcribed Image Text:You have a new internship, where you are helping to design a new freight yard for the train station in your city. There will be a number of dead-end sidings where single cars can be stored until they
are needed. To keep the cars from running off the tracks at the end of the siding, you have designed a combination of two coiled springs as illustrated in the figure below. When a car moves to the
right in the figure and strikes the springs, they exert a force to the left on the car to slow it down.
k2
ki
A single railcar is shown on the rail tracks. To its right,
but not connected to it, is a combination of two
horizontal, coiled springs - one, labeled k,, is broader
and shorter and the other, labeled k,, is narrower and
longer. Both the springs are connected to a vertical
surface.
To tal force (N)
2000-
1500
1000
500
Distance (cm)
60
10
20
30
40
50
Both springs are described by Hooke's law and have spring constants k, = 1,800 N/m and k, = 2,800 N/m. After the first spring compresses by a distance of d = 30.0 cm, the second spring acts with
the first to increase the force to the left on the car in the figure. When the spring with spring constant k, compresses by 50.0 cm, the coils of both springs are pressed together, so that the springs can
%3D
no longer compress. A typical car on the siding has a mass of 7,000 kg. When you present your design to your supervisor, he asks you for the maximum speed (in m/s) that a car can have and be
stopped by your device.
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