1. A 1,661-kilogram roller coaster car starts at point A almost at rest. It runs

Question

1. A 1,661-kilogram roller coaster car starts at point A almost at rest. It runs downhill into a valley. At its bottom, the valey can be described by a circle with radius 7 m. Find the height required at point A, such that the normal force acting on the car in point B is 333% of the weight.

2. A 1,896-kilogram roller coaster car starts at point A almost at rest. It first runs downhill and then is approaching a hill. At its top, the hill can be described by a circle with radius 8 m.

Find the height required at point A, such that the normal force acting on the car in point B is 51% of the weight.

Explanation / Answer

Noral force at the bottom N = mg + mv^2/r

since N is 333%

N = 3.33 mg

so

change in KE = PE

0.5 mv^2 = mgh

N = mg + 2 mgh/r

3.33 mg = mg + 2mgh/r

2.33 mg = 2mgh/r

h = 2.33/2 * r

h = 2.33* 7/2

h = 8.155 m

-----------------------------------

Noral force at the bottom N = mg - mv^2/r

since N is 51%

N = 0.51 mg

so

change in KE = PE

0.5 mv^2 = mgh

N = mg - 2 mgh/r = 0.51

0.51 mg = mg - 2mgh/r

(1-0.51) mg = 2mgh/r

h = 0.49/2 * r

h = 0.49* 8/2

h = 1.96 m

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

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