Find the change in thermal energy of the system. *Note: The region under the spring also has gravel under it.*

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You are designing a runaway truck ramp for Interstate 70 near Dillon. The setup is shown below.
spring
gravel
The hill is covered in gravel so that the truck's wheels will slide up the hill instead of rolling up the hill. The coefficient of kinetic friction
between the tires and the gravel is uk. This design has a spring at the top of the ramp that will help to stop the trucks. This spring is
located at height h. The spring will compress until the truck stops, and then a latch will keep the spring from decompressing (stretching
back out). The spring can compress a maximum distance x because of the latching mechanism. Your job is to determine how strong the
spring must be. In other words, you need to find the spring constant so that a truck of mass mt, moving at an initial speed of vo, will be
stopped. For this problem, it is easiest to define the system such that it contains everything: Earth, hill, truck, gravel, spring, etc. In all of
the following questions, the initial configuration is the truck moving with a speed of vo on the level ground, and the final configuration is
the truck stopped on the hill with the spring compressed by an amount x. The truck is still in contact with the spring. *Solve all of the
questions algebraically first. Then use the following values to get a number for the desired answer.*
Transcribed Image Text:You are designing a runaway truck ramp for Interstate 70 near Dillon. The setup is shown below. spring gravel The hill is covered in gravel so that the truck's wheels will slide up the hill instead of rolling up the hill. The coefficient of kinetic friction between the tires and the gravel is uk. This design has a spring at the top of the ramp that will help to stop the trucks. This spring is located at height h. The spring will compress until the truck stops, and then a latch will keep the spring from decompressing (stretching back out). The spring can compress a maximum distance x because of the latching mechanism. Your job is to determine how strong the spring must be. In other words, you need to find the spring constant so that a truck of mass mt, moving at an initial speed of vo, will be stopped. For this problem, it is easiest to define the system such that it contains everything: Earth, hill, truck, gravel, spring, etc. In all of the following questions, the initial configuration is the truck moving with a speed of vo on the level ground, and the final configuration is the truck stopped on the hill with the spring compressed by an amount x. The truck is still in contact with the spring. *Solve all of the questions algebraically first. Then use the following values to get a number for the desired answer.*
mt = 19000 kg
vo = 64 m/s
x = 3 meters
h = 47 meters
Hk = 0.62
0 = 33.1 degrees
L = 10.8 meters
W
Ug
Et
Find the change in thermal energy of the system. *Note: The region under the spring also has gravel under it.*
ΔΕnerm
3659327.409 N*i
>> <
Transcribed Image Text:mt = 19000 kg vo = 64 m/s x = 3 meters h = 47 meters Hk = 0.62 0 = 33.1 degrees L = 10.8 meters W Ug Et Find the change in thermal energy of the system. *Note: The region under the spring also has gravel under it.* ΔΕnerm 3659327.409 N*i >> <
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