A drive Wheel. A drive wheel, with centre O and radius 0.5 m, rotates at 4 full

Question

A drive Wheel.

A drive wheel, with centre O and radius 0.5 m, rotates at 4 full revolutions per second. It is connected as shown to a piston by a connecting rod QP of length 2 m. Use the cosine rule to obtain an equation connecting the distance x, the angle theta and the other lengths in the problem. (You do not| need to solve this equation to find x.) By implicitly differentiating the equation found above with respect to t, obtain a relationship between x, theta, d theta/dt, dx/dt and the various lengths in the problem. How fast is the piston moving when x = 2.1 m? (Give your answer in m s-1 to 3 significant figures.)

Explanation / Answer

(i) PQ^2=OQ^2 + PO^2 - 2*OQ*PO*cos(O)

x^2=2cos(theta) + 3.7

(ii) 2*x*dx/dt=-2sin(theta)*d(theta)/dt

(iii

1 mint=4*60=240 rev.F=240 rpmd/dt(theta)=w=2*pie*N/60w=25rad/sx=2.1theta=76 degree2*2.1*dx/dt=-2*sin(76)*25.1

v=11 m/s(-)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.