Question

5. For this series of 4 questions, a rider rides in a car that is connected to a 4-m rod, and rotates about the z axis. The rod of negligible mass is subjected to a constant couple moment of M, and the engine of the car supplies a traction force of F. Neglect the size of the car. You will be asked to solve for different things. Please pay attention: the numbers may change from problem to problem since they are randomized. 3) If the rod is subjected to a constant couple moment of M = 900 N·m, and the engine of the car supplies a traction force of F=14•t N to the wheels, where tis in seconds, what is the magnitude of the angular impulse from the moment and the force to the car-rider system in kg•m2/s from t = 0 to t= 5.8 s? Your answer must include 1 place after the decimal point. z 4 m M

Answer 1

Total angular impulse is given as;

$H_z = \sum \int M_z dt$

$\Rightarrow H_z = \int _o^t Mdt + \int _o^t FRdt$

$\Rightarrow H_z = M\int _o^t dt + R\int _o^t Fdt$

$\Rightarrow H_z = M\int _o^{5.8} dt + R\int _o^{5.8} (14t)dt$

$\Rightarrow H_z = (900)\int _o^{5.8} dt + (4)\int _o^{5.8} (14t)dt$

$\Rightarrow H_z = (900)(5.8-0)+ (4\times14)\left ( \frac{5.8^2-0^2}{2} \right )$

$\Rightarrow H_z = 6161.9\;\;kg.m^2/s$

$\Rightarrow H_z = \mathbf{6161.9}$

...(Answer)