A Hot Wheels car of mass 0.081 kg starts at a height of 1.42 m and goes through a loop with a height of 0.38 m with a radius of 0.16 m along a track of length 3.02 m. The car barely makes it through the loop. Since, Work = Force x distance, what is the force of friction acting upon the car?
To find the force of friction acting upon the Hot Wheels car, we first need to calculate the work done on the car.
The work done on an object is equal to the product of the force acting on the object and the distance over which the force is applied. In this case, the force we are interested in is the force of friction.
The work done on the car is given by the equation:
Work = Force x Distance
Since the car barely makes it through the loop, it means that the work done on the car is equal to zero. This implies that the net work on the car is zero, and therefore, the work done by friction is equal in magnitude but opposite in sign to the work done by gravity.
The work done by gravity can be calculated as the change in potential energy of the car as it moves from a height of 1.42 m to 0.38 m:
Work_gravity = m * g * (change in height)
where m is the mass of the car (0.081 kg), g is the acceleration due to gravity (9.8 m/s^2), and (change in height) is the difference in height (1.42 m - 0.38 m = 1.04 m).
Substituting the values into the equation, we get:
Work_gravity = 0.081 kg * 9.8 m/s^2 * 1.04 m
Now, since the net work on the car is zero, the work done by the force of friction can be calculated as the negative of the work done by gravity:
Work_friction = - Work_gravity
Substituting the value of Work_gravity, we get:
Work_friction = - (0.081 kg * 9.8 m/s^2 * 1.04 m)
Finally, since Work_friction = Force_friction * distance, we can rearrange the equation to solve for the force of friction:
Force_friction = - (Work_friction / distance)
Given that the distance is 3.02 m, we can substitute the values into the equation to find the force of friction.