# Physics

posted by .

The roller coaster starts with a velocity of 16 m/s. One of the riders is a small girl of mass 26 kg. Find her apparent weight when the roller coaster is at locations B and C. At these two locations, the track is circular, with the radii of curvature given.

rB = 10 m,
rC = 20 m,

The heights at points A, B, and C are
hA = 22 m,
hB = 32 m,
and
hC = 0.

Assume friction is negligible and ignore the kinetic energy of the wheels. (The figure is not necessarily drawn to scale.)

What is the weight at B?

• Physics -

Point A: h₁= 22 m, v₁=16 m/s;
Point B: h₂= 32 m, r₂= 10 m, v₂=?;
Δh₁₂ = h₂-h₁=32-22 = 10 m;
Point C: h₃=0, r₃= 20 m, v₃=?;
Δh₂₃ = h₂-h₃ = 32 – 0 = 32 m.

KE₁+PE₁=PE₂ + KE₂,
mv₁²/2 +mgh₁=mgh₂ +mv₂²/2,
mv₁²/2= mv₂²/2+ mgh₂ - mgh₁=
=mv₂²/2+ mg Δh₁₂.
v₂ = sqrt{ v₁²- 2gΔh₁₂} =
=sqrt{16² - 2•9.8•10} =7.75 m/s.

For point B:
ma₂=mg-N₂,
N₂=mg-ma₂=m[g- (v₂²/r₂)]=
= 26[ 9.8 – (7.75²/10)]= 98.8 N,
N₂ (normal force) = W₂ (weight)
W₂= 98.8 N.

PE₂ +KE₂ = PE₃+KE₃,
mgh₂ +mv₂²/2 = mgh₃ +mv₃²/2,
mv₃²/2 = mgh₂ +mv₂²/2 - mgh₃=
=mv₂²/2 + mg Δh₂₃ ,
v₃ = sqrt{v₂² +2g Δh₂₃}=
=sqrt{ 7.75² + 2•9.8•32) = 26.2 m/s.

For point C:
ma₃= N₃ – mg,
N₃= mg+ma₃=m[g+ (v₃²/r₃)]=
= 26[ 9.8 + (26.2²/20)]= 1148.2 N.
N₃ (normal force) = W₃ (weight)
W₃= 1148.2 N.

## Similar Questions

1. ### Physics

we are doing a really dumb websearch in my Physics class on roller coasters and I really need help with like 5 problems! For the websearch I need to cite it so if you could provide any answers I also need the website! thanks in advance!!! …
2. ### physics

A roller coaster of mass 1000.0 kg passes point A with a speed of 1.80 m/s?
3. ### College Physics

The roller coaster in Figure P6.36 starts with a velocity of 15.4 m/s. One of the riders is a small girl of mass 30 kg. Find her apparent weight when the roller coaster is at locations B and C. At these two locations, the track is …
4. ### Physics 1

Consider a roller coaster that moves along the track shown in the figure below. Assume all friction is negligible and ignore the kinetic energy of the roller coaster's wheels. Assume the roller coaster starts with a speed of 19 m/s …
5. ### Repost-Physics 1

Consider a roller coaster that moves along the track shown in the figure below. Assume all friction is negligible and ignore the kinetic energy of the roller coaster's wheels. Assume the roller coaster starts with a speed of 19 m/s …
6. ### Physics

A student has a weight of 650 N. While riding on a roller-coaster this same student has an apparent weight of 1.97 x 103 N at the bottom of a loop that has a radius of 17.0 m. The speed of the roller-coaster is I just need the forumla, …
7. ### PHYSICS

The roller coaster in the figure below starts with a velocity of 17 m/s. One of the riders is a small girl of mass 31 kg. Find her apparent weight when the roller coaster is at locations B and C. At these two locations, the track is …
8. ### Science

Can you Describe what happens when a roller coaster rolls downhill in terms of velocity and acceleration. Is the roller coaster increasing in velocity?
9. ### Science

The Millennium Force is the highest roller coaster in North America. It reached a maximum height to 94.5 m. The total mass of the roller coaster car and its passengers is 1380 kg. The speed of the roller coaster is 41.1 m/s at its …
10. ### Physics

a 4,500 kg roller coaster starts from the top of a 45 m hill with a velocity of 3m/s. The car travels to the bottom through a loop and continues up the next hill. The end of the roller coaster has a level surface that is 4m off the …

More Similar Questions