Download Application of Newton`s Laws Circular Motion Answers

Application of Newton’s Laws Circular Motion Answers
1) Find the sum of all the forces in the x direction.
Then substitute for the friction and the acceleration:
Now we should look at the forces in the y direction.
Solve for the normal force:
Substitute the normal force into the x direction equation.
Now substitute the numerical values to determine v:
2) There are four ideas that relate to the force on the car:
a. A centripetal force must act on the car if it is moving in a circular path.
b. The only horizontal force acting on the car is the frictional force, so the centripetal
force is the frictional force.
c. The frictional force must be static friction since the car is not sliding.
d. Since the car is on the verge of sliding the force will be the maximum frictional force.
The centripetal force on the car is:
Solve this for
:
Then substitute the numerical values to find the coefficient of friction:
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3) First you need to find the forces in the y direction and set it equal to zero:
Solve for N:
The only force in the x direction is the centripetal force:
Then do a substitution of in the above equation:
Now solve for theta:
And substitute the numerical values:
4) Find all the forces in the y direction:
5) At the top of the loop the forces acting on the rider are gravity and the normal force.
These forces need to be equal to the centripetal force.
Now, if the bicycle is about to drop then the normal force is equal to zero. Then solving
for v: