Question

The Model : Consider a block on an inclined plane. The block is subject to weight, friction, and drag forces. Fweight = mxg Fdrag = Cdrag XV, Ffriction = Mfriction X Fnormal Constant Parameters : • mass, m = 20 kg • Drag Coefficient, Cdrag = 2.5 Womens • gravity, g = 9.8 ? • Friction Coefficient, Mfriction = 0.75 • angle, 0 = 55°

Answer 1

mg*sin(theta) Freight = mg mg*cos(theta) = F normal Fdrag = Cdrag X X Ffriction = Mfriction X Fnormal

(Fr) = 0

Expressing in terms of v

ODE :-

201 + 2.5 V 7.2381 By Trial Solution method let, Volt A as R.H. 3. is constant Substituting in ODE. 20 (0) + 2.5(A) = 46.2381 A = 76.2381. Vpc 96.238 25 Komplimentary function V ) :- CF is found from associated bewegen.com luation - 200+ 2.5 V = 0 & + 2.5 Vox o Auxillary equation AE: + 2.5= Then CE, VACt) - ceno → VCE) - cest Hence. Solutio. 25 TVCH) : Geo + 16.2381 VO) - (-) * O Grey) 7602381 25 → C = -76,2381 25

Substituting in Vit). VC - - 76.2381 e + 46.2291 25 3. z XCH) = SV(t) do ta 16.3581 -fedt + fest] + c 25 -87 36.2281 Itt ta 25 1-1/8 276-2381 [_et/ 8 17. ++ + c 25 19 r(t) = 76.23818 pttt a 25 it., (c) = 0 25 0 = 16.23e18 25 C = - 8x6.2281 (t) = 76.2281 se 25

Matlab Code to plot :-

a = 76.2381/25; Defining the ratio as constant to reduce typing efforts Expression for velocity of block = @(t) -a*exp(-t/8) + a; v Expression for position of block x = @(t) a* (**exp(-t/s) + t - 8); Ploting subplot (2,1,1) $ 13t subplot Eplot(x, [0, 301) ploting x(t) for t in range (0,30) vlabel ("Position, X(t) [m] ") title("Position of block vs. Time") grid on subplot(2,1,2) 2nd subplot Eplot (v, [0, 301) ploting v(t) for t in [0 30] ylabel("Velocity, v(t) [m/ 3]") xlabel("time (t)") title("Velocity of block vs. Time") grid on

a = 76.2381/25; % Defining the ratio as constant to reduce typing efforts

% Expression for velocity of block
v = @(t) -a*exp(-t/8) + a;

% Expression for position of block
x = @(t) a*(8*exp(-t/8) + t - 8);

% Ploting
subplot(2,1,1) % 1st subplot
fplot(x,[0,30]) % ploting x(t) for t in range (0,30)
ylabel("Position, x(t) [m]")
title("Position of block vs. Time")
grid on

subplot(2,1,2) % 2nd subplot
fplot(v,[0,30]) % ploting v(t) for t in [0 30]
ylabel("Velocity, v(t) [m/s]")
xlabel("time (t)")
title("Velocity of block vs. Time")
grid on

Position of block vs. Time Position, X(t) [m] - הט 10 15 1 20 25 30 Velocity of block vs. Time Velocity, v(t) [m/s] 10 20 25 30 15 time (t)