You and a friend from high school are off-roading through Ocala National Forest in your friend’s Jeep (mass of 1800 kg), when a Florida panther runs onto the path. You swerve to miss the panther, but slide into a muddy ditch and get stuck. Luckily, your friend has a winch on their Jeep, which you connect to a tree as shown in the figure. The ground between the Jeep and the tree has a steady slope with an angle of 5 degrees, and the coefficient of kinetic friction between the muddy ground and the rubber tires is 0.15. Consider that the winch is being used to pull the Jeep out of the ditch at a steady speed. a. How much does the gravitational potential energy (in Joules) of the Jeep change as it is pulled a distance of 5 m up the slope? b. How much work (in Joules) is done by the tension force in the winch as it pulls the Jeep a distance of 5 m up the slope? c. If the maximum power output of the winch is 6.6 horsepower (about 5000 W), what is the maximum speed (in m/s) at which the Jeep can be pulled from the ditch?
You and a friend from high school are off-roading through Ocala National Forest in your friend’s Jeep (mass of 1800 kg), when a Florida panther runs onto the path. You swerve to miss the panther, but slide into a muddy ditch and get stuck. Luckily, your friend has a winch on their Jeep, which you connect to a tree as shown in the figure. The ground between the Jeep and the tree has a steady slope with an angle of 5 degrees, and the coefficient of kinetic friction between the muddy ground and the rubber tires is 0.15.
Consider that the winch is being used to pull the Jeep out of the ditch at a steady speed.
a. How much does the gravitational potential energy (in Joules) of the Jeep change as it is pulled a distance of 5 m up the slope?
b. How much work (in Joules) is done by the tension force in the winch as it pulls the Jeep a distance of 5 m up the slope?
c. If the maximum power output of the winch is 6.6 horsepower (about 5000 W), what is the maximum speed (in m/s) at which the Jeep can be pulled from the ditch?
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