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exis [7]
3 years ago
5

A car of mass 1230 kg is on an icy driveway inclined at an angle of 39°. The acceleration of gravity is 9.8 m/s². θ If the incli

ne is friction-less, what is the acceleration of the car? Answer in units of m/s².
Physics
1 answer:
tamaranim1 [39]3 years ago
6 0

Answer:

Acceleration of the car, a=6.16\ m/s^2

Explanation:

It is given that,

Mass of the car, m = 1230 kg

The car is inclined at an angle of 39 degrees.

The acceleration of gravity acting on the car is 9.8\ m/s^2. The component of car parallel to inclined planes is :

W_x=mg\ sin\theta

Net force acting on it is :

ma=mg\ sin\theta

a=g\ sin\theta

a=9.8\times \ sin(39)

a=6.16\ m/s^2

So, the acceleration of the car is 6.16\ m/s^2. Hence, this is the required solution.

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A crude approximation for the x component of velocity in an incompressible laminar boundary layer is a linear variation from u =
slega [8]

Answer:

2.5 * 10^-3

Explanation:

<u>solution:</u>

The simplest solution is obtained if we assume that this is a two-dimensional steady flow, since in that case there are no dependencies upon the z coordinate or time t. Also, we will assume that there are no additional arbitrary purely x dependent functions f (x) in the velocity component v. The continuity equation for a two-dimensional in compressible flow states:

<em>δu/δx+δv/δy=0</em>

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<em>δv/δy= -δu/δx</em>

Now, since u = Uy/δ, where δ = cx^1/2, we have that:

<em>u=U*y/cx^1/2</em>

and we obtain:  

<em>δv/δy=U*y/2cx^3/2</em>

The last equation can be integrated to obtain (while also using the condition of simplest solution - no z or t dependence, and no additional arbitrary functions of x):  

v=∫δv/δy(dy)=U*y/4cx^1/2

 =y/x*(U*y/4cx^1/2)

 =u*y/4x

which is exactly what we needed to demonstrate.  

Also, using u = U*y/δ in the last equation we can obtain:  

v/U=u*y/4*U*x

     =y^2/4*δ*x

which obviously attains its maximum value for the which is y = δ (boundary-layer edge). So, finally:

(v/U)_max=δ^2/4δx

                =δ/4x

                =2.5 * 10^-3

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