In the simulation on the right, you are asked to race a truck on an S-shaped tra
ID: 2245674 • Letter: I
Question
In the simulation on the right, you are asked to race a truck on an S-shaped track against the computer. This time, the first curve is covered with snow and you are racing against a snowmobile. As you go around the track, the static friction between the tires of your truck and the snow or pavement provides the centripetal force. If you go too fast, you will exceed the maximum force of friction and your truck will leave the track. If you go as fast as you can without sliding, you will beat the snowmobile.
The snowmobile runs the entire race at its maximum speed. The blue truck negotiates each curve at a constant speed, but these speeds must be different for you to win the race. You set the speed of the blue truck on each curve. Straightaway sections are located at the start of the race and between the two curves. The simulation will automatically supply the acceleration you need on the straightaway sections.
The blue truck has a mass of 1,800 kg. The first curve is icy, and the coefficient of static friction of the truck on this curve is 0.51. (The snowmobile has a greater coefficient thanks to its snow-happy treads.) On the second curve, the coefficient of static friction is 0.84. The radius of the first curve is 13 m, and the second curve is 11 m. Set the speed of the blue truck on each curve as fast as it can go without sliding off the track, and you will win.
PLEASE SHOW ALL WORK AND ***EXPLAIN the reasoning***. I have the answers, but I am trying to learn how to solve this problem.
Explanation / Answer
Here
Centripetal Forrce is provided by the Frictional Force
Therefore
mv^2/r = umg
Therefore
v = sqrt(urg)
For r = 13 m
v = sqrt(0.51*13*9.8)
= 8.06 m/sec
For r = 11 m
v = sqrt(0.51*11*9.8)
= 7.41 m/sec