A roller-coaster car rolls down a frictionless track, reaching speed v0 at the bottom. If you want the car to go twice as fast at the bottom, by what factor must you increase the height of the track? Explain.
As the speed depends only on the vertical height and not the shape of the track, the height of the track is increased by two times.
As we know the track is frictionless, let us consider the car and Earth as an isolated system. So, firstly find the equation of the final velocity at the bottom, when the car starts from the rest at height h.
Note that car starts from rest, , because it is at ground and
To make car go twice as fast at the bottom, we will use above equation.
An object moving in the xy-plane is subjected to the force , where x and y are in m.
a. The particle moves from the origin to the point with coordinates by moving first along the x-axis to , then parallel to the y -axis. How much work does the force do?
b. The particle moves from the origin to the point with coordinates by moving first along the y-axis to , then parallel to the x -axis. How much work does the force do?
c. Is this a conservative force?
The spring shown in FIGURE P10.54 is compressed and used to launch a physics student. The track is frictionless until it starts up the incline. The student’s coefficient of kinetic friction on the incline is .
a. What is the student’s speed just after losing contact with the spring?
b. How far up the incline does the student go?
Object is stationary while objects are in motion. Forces from object of work on object of work on object . Forces from the environment do of work on object of work on object . Objects do not interact. What are if
(a) objects are defined as separate systems and
(b) one system is defined to include objects and their interactions?
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