Question

If the angle θ=θ= 30 ∘∘ , determine the acceleration of the truck. The coefficient of kinetic friction between the pipe and the ground is μk=0.20μk=0.20.

MasteringEngineering Masterir x + session.masteringengineering.com/myct/itemView?assignmentProblemlD=11226089 H MAE 242 Summer 2020 Hader 3 CME HW10 Problem 17.52 6 of 15 A Review The pipe has a mass of 870 kg and is being towed behind a truck (Figure 1) Part A If the angle A = 30°, determine the acceleration of the truck. The coefficient of kinetic friction between the pipe and the ground is ili = 0.20. Express your answer to three significant figures and include the appropriate units. NHÀ o ? a = Value Units Submit Request Answer Figure Part B 1 of 1 Also, determine the tension in the cable. Express your answer to three significant figures and include the appropriate units. ? T = Value Units 0.4m Submit Request Answer Provide Feedback Next >

Answer 1

T mg 14 T 0.4 m 0.4 m ma q 0.2N IN

Taking moment about G;

$\sum M_G = 0$

$\Rightarrow Tsin(45^o-30^o)(0.4) - 0.2N(0.4) = 0$

$\Rightarrow N = 1.2941T$

Equilibrium of forces;

$\sum F_y = 0$

$\Rightarrow N - 870(9.81)+Tsin45^o = 0$

$\Rightarrow 1.2941T - 870(9.81)+Tsin45^o = 0$

$\Rightarrow T = 4264.787\;\;N$

and

$\sum F_x = ma$

$\Rightarrow Tcos45^o - 0.2N = 870 a$

$\Rightarrow Tcos45^o - 0.2(1.2941T) = 870 a$

$\Rightarrow (4264.787)cos45^o - 0.2(1.2941\times4264.787) = 870 a$

$\Rightarrow a = 2.20\;\;m/s^2$

Answer: