- #1

Crunge

- 11

- 4

- Homework Statement
- The tangential velocity ,vt, for the cart of a ferris wheel varies with time according to vt(t)= k*t. Assume that the constant k = 0,695 m/s^2 and that the radius of the ferris wheel is 11,7 m.

What is the sum of the cart acceleration after 3,32 seconds?

- Relevant Equations
- (The equations I have tried to use)

vt(t) = k*t

radial acceleration: (instantaneous) ar = (v^2) / t

angular velocity: ω = v/r

angular acceleration (average): α = Δω/Δt

angular acceleration (instantaneous): α = 1/T^2

T = 2π/ω

tangential acceleration: at = α*r

After 3,32 seconds, vt should have varied by 0,695*3,32. I have done a previous exercise where you only needed to calculate the radial acceleration in this scenario. There, I took the vt after the given time, squared it and then divided with the radius. I remember clearing that one, so in this exercise I would think to do the same. Take 0,695*3,32, square the product and divide by 11,7 (the radius). Ends up being roughly 0,455.

But then I am having trouble getting the right tangential acceleration. I have also done an exercise where you calculate tangential accelaration, which I completed, but in this one I can't seem to get the right answer no matter how I go about calculating the tangential acceleration.

First the formula for average angular acceleration: ω = v/r. In this problem, I think Δω should simply be (k*t)/r since the linear velocity varies according to k*t. Δt should be 3,32 seconds, according to what the problem defined. With this, I calculated α with Δω/Δt. If I then use at = α*r,

I as expected end up with 0,695, the same value as k. This seems suspicious, though it is undoubtebly where I end up using these equations. This is the result you get if you calculate the acceleration as linear as well, both average and instantaneous. (Δv/Δt), or d/dt * v(t). Though if I add the radial and tangential acceleration together I get the wrong answer.

I eventually tried to use the formula for instantaneous angular acceleration. ω is yet again (0,695*3,32)/11,7. T should then be 2π/ω, which I then square and inverse according to α = 1/T^2. Lastly I multiply with 11,7 according to at = α*r. This of course ends up with a suspiciously small number which also doesn't give the right answer when added to the radial acceleration.

From this point, try as I might, I can't think of another way to go about this problem. I feel like the strategies I tried first have worked before in other exercises. My best guess is that there's something about that formula vt = k*t, that I am not getting. Maybe the fact that it describes how vt

But then I am having trouble getting the right tangential acceleration. I have also done an exercise where you calculate tangential accelaration, which I completed, but in this one I can't seem to get the right answer no matter how I go about calculating the tangential acceleration.

First the formula for average angular acceleration: ω = v/r. In this problem, I think Δω should simply be (k*t)/r since the linear velocity varies according to k*t. Δt should be 3,32 seconds, according to what the problem defined. With this, I calculated α with Δω/Δt. If I then use at = α*r,

I as expected end up with 0,695, the same value as k. This seems suspicious, though it is undoubtebly where I end up using these equations. This is the result you get if you calculate the acceleration as linear as well, both average and instantaneous. (Δv/Δt), or d/dt * v(t). Though if I add the radial and tangential acceleration together I get the wrong answer.

I eventually tried to use the formula for instantaneous angular acceleration. ω is yet again (0,695*3,32)/11,7. T should then be 2π/ω, which I then square and inverse according to α = 1/T^2. Lastly I multiply with 11,7 according to at = α*r. This of course ends up with a suspiciously small number which also doesn't give the right answer when added to the radial acceleration.

From this point, try as I might, I can't think of another way to go about this problem. I feel like the strategies I tried first have worked before in other exercises. My best guess is that there's something about that formula vt = k*t, that I am not getting. Maybe the fact that it describes how vt

*varies*has some significance that I am not picking up on.