A bicyclist is attempting a loop-the-loop stunt, in which she will coast around

Question

A bicyclist is attempting a loop-the-loop stunt, in which she will coast around a track shaped into a
vertical circle with a radius of 7.2 m.
If the bike and rider enter the loop at the bottom with a speed of 17 m/s, will they be able to coast all
the way around the loop? Ignore air resistance.
Physics & Derivation
The bike is not in free fall! The track exerts a changing normal force on it as it loops around, so not
only does it not have the free-fall acceleration, it doesn't even have a constant acceleration as it rises
and slows down. Lacking a known, constant acceleration, the methods of kinematics won't work. For a
valid derivation, use only equations taken from the Work & energy section of the equation sheet.

Explanation / Answer

If we assume that the origin is at the base of the loop, The maximum energy being brought into the system is all kinetic KE = ½mv² At the top of the loop, some of the energy will be converted to potential energy PE = mgh The difference should be the remaining kinetic energy. KEi = mgh + KEf ½mvi² = mgh + ½mvf² ½mvi² - mgh = ½mvf² vi² - 2gh = vf² vf = v(vi² - 2gh) vf = v(17² - 2(9.81)7.2) vf = 12.2 m/s as this is greater than the minimum allowable velocity, the loop can be successfully completed.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.