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 = 740 N·m, and the engine of the car supplies a traction force of F=10 t N to the wheels, where t is 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 = 6.7 s? Your answer must include 1 place after the decimal point. Z 4 m M F

Answer 1

We have,
Radius
→ R= 4 m

Constant couple moment $\rightarrow M=740\ Nm$
Traction force
→ F= 100 N

Initial time $\rightarrow t_{1}=0\ s$
Final time $\rightarrow t_{2}=6.7\ s$

The angular impulse is given as:

$H=\sum \int_{t_{1}}^{t_{2}}M\ dt$

$\therefore H= \int_{t_{1}}^{t_{2}}M\ dt+\int_{t_{1}}^{t_{2}}FR\ dt$

$\therefore H=M+R\int_{t_{1}}^{t_{2}}10t\ dt$

$\therefore H=M+10R\int_{0}^{6.7}t\ dt$

$\therefore H=M+10R \left (\left (\frac{t^{2}}{2} \right ) ^{6.7}_{0} \right )$

$\therefore H=M+10R\ ((6.7^{2}/{2} )-(0^{2}/{2} ) )$

$\therefore H=740+(10\times4\times (22.445))$

${\color{Blue} \therefore H=1637.8\ kg\ m^{2}\ s^{-1}}$

Therefore, the magnitude of angular impulse on the raider from the angular momentum is ${\color{Blue} H=1637.8\ kg\ m^{2}\ s^{-1}}$ .