Question

Problem 3 - Roller Coaster A roller coaster slides down a curved ramp which is shown below. The wheels of the coaster car are built using high quality sealed ball bearings which apply a small torque resulting in friction. This friction is mostly due to the rolling resistance for surfaces inside of the bearing and internal lubrication. Lets approximate this friction to be a constant $f$. The cart is pulled to the top of the first hill at a height $h_1$, rolls over the peak at a speed of $|v_1|$. The cart then falls down the first hill, passes through a curve of radius $R$ to a minimum height of $h_3$ at the bottom, and then raises up the second hill to a height of $h_2$. The total length of the track (path length) between the top of the two hills is $l = h_1 + h_2 + 3R$. Pick the following variables (different from your friends/partners): \begin{itemize} \item heights $h_1$ and $h_2$ for each of the first hills. \item Radius of the loop $R$ \item Initial velocity $v_i$ \item force of friction $f$ measured in Newtons \item Mass of the cart \end{itemize} Problem: Calculate the speed of the cart at the top of the second ramp. Calculate the speed at the bottom of the valley and the g-force felt by a rider.

          Problem 3 - Roller Coaster
A roller coaster slides down a curved ramp which is shown below. The wheels of the coaster car are built
using high quality sealed ball bearings which apply a small torque resulting in friction. This friction is mostly
due to the rolling resistance for surfaces inside of the bearing and internal lubrication. Lets approximate
this friction to be a constant $f$.
The cart is pulled to the top of the first hill at a height $h_1$, rolls over the peak at a speed of $|v_1|$. The cart
then falls down the first hill, passes through a curve of radius $R$ to a minimum height of $h_3$ at the bottom,
and then raises up the second hill to a height of $h_2$. The total length of the track (path length) between the
top of the two hills is $l = h_1 + h_2 + 3R$.
Pick the following variables (different from your friends/partners):
\begin{itemize}
    \item heights $h_1$ and $h_2$ for each of the first hills.
    \item Radius of the loop $R$
    \item Initial velocity $v_i$
    \item force of friction $f$ measured in Newtons
    \item Mass of the cart
\end{itemize}
Problem: Calculate the speed of the cart at the top of the second ramp. Calculate the speed at the
bottom of the valley and the g-force felt by a rider.

Problem 3 - Roller Coaster
A roller coaster slides down a curved ramp which is shown below. The wheels of the coaster car are built
using high quality sealed ball bearings which apply a small torque resulting in friction. This friction is mostly
due to the rolling resistance for surfaces inside of the bearing and internal lubrication. Lets approximate
this friction to be a constant f.
The cart is pulled to the top of the first hill at a height h1, rolls over the peak at a speed of |v1|. The cart
then falls down the first hill, passes through a curve of radius R to a minimum height of h3 at the bottom,
and then raises up the second hill to a height of h2. The total length of the track (path length) between the
top of the two hills is l = h1 + h2 + 3R.
Pick the following variables (different from your friends/partners):

* heights h1 and h2 for each of the first hills.

* Radius of the loop R

* Initial velocity vi

* force of friction f measured in Newtons

* Mass of the cart

Problem: Calculate the speed of the cart at the top of the second ramp. Calculate the speed at the
bottom of the valley and the g-force felt by a rider.

Added by Zachary A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Neelesh Sharma

03/18/2022

Step 1

- Use conservation of energy to calculate the speed at the top of the second ramp. The initial potential energy at the top of the first hill is converted into kinetic energy at the bottom of the first hill, then potential energy at the bottom of the valley, and Show more…

Show all steps

Thanks for your feedback!

Problem 3 - Roller Coaster A roller coaster slides down a curved ramp which is shown below. The wheels of the coaster car are built using high quality sealed ball bearings which apply a small torque resulting in friction. This friction is mostly due to the rolling resistance for surfaces inside of the bearing and internal lubrication. Lets approximate this friction to be a constant f. The cart is pulled to the top of the first hill at a height h_(1), rolls over the peak at a speed of |vec(v)_(i)|. The cart, then falls down the first hill, passes through a curve of radius R to a minimum height of h_(3) at the bottom, and then raises up the second hill to a height of h_(2). The total length of the track (path length) between the top of the two hills is l=h_(1)+h_(2)+3R. Pick the following variables (different from your friends/partners): heights h_(1) and h_(2) for each of the first hills. Radius of the loop R Initial velocity v_(1) force of friction f measured in Newlons Mass of the cart Problem: Caleulate the speed of the cart at the top of the recond ramp. Calculate the speed at the bottom of the valley and the g-force felt by a rider. Discussion Questions Problem 3-Roller Coaster A roller coaster slides down a curved ramp which is shown below. The whecls of the coaster car are built using high quality sealed ball bearings which apply a small torque resulting in friction. This friction is mostly due to the rolling resistance for surfaces inside of the bearing and internal lubrication. Lets approximate this friction to be a constant f. The cart is pulled to the top of the first hill at a height h1,rolls over the peak at a specd of |u.The cart then falls down the first hill,passes through a curve ol radius R to a minimum height of h3 at the bottom and then raises up the second hill to a height ol h2.The total length of the track (path length) between the topof the two hills is l-hi+h+3R. Pick the following variables (different from your friends/partners): heights hi and h for each of the first hills Radius of the loop R 4 Initial velocity force of friction f mcasured in Newions Mass of the cart Problem: Calculate the speed of the cart at the top of the second ramp. Calculate the spced at the bottom of the valley and the g-force felt by a rider Path T R h. h, Discussion Questions

Play audio

Feedback

Neelesh Sharma and 88 other subject Physics 103 educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 Okay friends, this is a roller coaster ride of last 250 cm.

00:11 Of which there is a slant distance of 230 meters and the ending part is 20 meters.

00:17 So the roller coaster will be stopped after 250 meters distance.

00:23 So we are just naming this for east, a, b, c.

00:26 And now between a to b, there is a constant reducing fictional force that is applied of the value 350 newtons.

00:38 And there is also a fictional force applied on this part, but its value we have to find.

00:43 We don't know the value of it.

00:45 So in this case, both the parts are affected upon so that the roller coaster stops at point c.

00:53 The rest of the forces that this point will be at the highest potential.

00:59 So this height is given as 103 meters.

01:02 Meters and there will be a high potential here so the object will fall in from here and raising to the next level speed at this point now at this point there will be a constant reduction in the speed due to this reducing forces and then and this part also there will be a final reduction so that the velocity at this point will be zero so this is the whole scenario now we'll see this step by step first is the constant friction of force required at this point so we have to find this f so we know the energy at the initial point this will be potential energy at a will be equal to the kinetic energy at c so this can be calculated by and plus the losses so what will the losses in this case the losses will be in the form of frictional forces and the kinetic energy at point c this is zero why it is zero because the v at c at c c is so the frictional losses are given in the form of forces.

02:13 So the force will be multiplied with the distance equivalent distance.

02:17 So for step by step, we'll take two parts of the frictional forces.

02:23 A .b.

02:24 Multiplied by its distance ab plus f, b, c multiplied by its distance b .c.

02:33 And what is the potential energy at this point? point a, it will be m g h, where m is given as 210, g is 9 .8, h is given as 103.

02:50 So this is the left hand side.

02:52 On the right hand side, the force is given as 350 newtons multiplied by the distance 230 plus the second force that we don't know value, multiplied by its distance of 20 meters.

03:05 So from here we can easily calculate the value of dc that comes out to be 6573 .7 nuitons.

03:16 Again, this is the first part.

03:19 So we got the value of the fictional force required.

03:22 In the second part we have, we need to find the maximum speed, the highest speed that will be reached and this highest speed will be at this point because this point has the highest kinetic energy.

03:35 That also will be lost till point c.

03:38 So b point will have the highest potential energy, highest kinetic energy and a point will have the highest potential energy.

03:45 So we are just equating that part.

03:47 So the potential energy at a is equal to the kinetic energy at b plus the losses, the frictional losses between ab multiplied by ab.

04:07 Getting you? so this is actually equal to the f bc part because this is the only the energy that is actually converted here so we can directly equate that part so f bc that we calculated earlier multiplied by bc is equals to the kinetic energy here half mv square okay and from here we'll get the velocity so f bc value we have already calculated 7 3 .7 multiplied by the d value d value is given as 20 is equal to half mass of the wagon is given as 1, 210 multiplied by its velocity.

04:47 So from here the velocity we are getting is actually 35 .38 meter per second.

04:56 This is the velocity at point b and this is the highest velocity towards existence.

05:04 Now again third part, in the third part we have to find the wagon is now now loaded so its mass initially the mass was 210 kg now the mass is added with 450kg additional weight so the total mass is now raised to 660kg correct now we are putting all of the calculations again so that we are getting the value so mgh the potential energy at a is equal to friction losses in ab multiplied by d of av, the frictional losses in b to c multiplied by d, b to c.

05:55 So again, this part is unknown because this is actually the variable frictional force that is applied as per the velocity.

06:04 If velocity is very high at point b, accordingly this frictional force will be very high.

06:08 So this we have to calculate again.

06:10 In this case, again, we'll use the same type...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later

Question

Please give Ace some feedback