Two identical wheels are moving on horizontal surfaces. The center of mass of ea

Question

Two identical wheels are moving on horizontal surfaces. The center of mass of each has the same linear speed. However, one wheel is rolling, while the other is sliding on a frictionless surface without rolling. Each wheel then encounters an incline plane. One continues to roll up the incline, while the other continues to slide up. Eventually they come to a momentary halt, because the gravitational force slows them down. Each wheel is a disk of mass 2.88 kg. On the horizontal surfaces the center of mass of each wheel moves with a linear speed of 5.76 m/s. (a),(b) What is the total kinetic energy of each wheel? (c), (d) Determine the maximum height reached by each wheel as it moves up the incline.

Explanation / Answer

a), b) The kinetic energy of the sliding wheel is KE1 = 1/2 m v^2 = 0.5 * 2.88* 5.76 * 5.76 = 47.77 J The kinetic energy of the rolling wheel is KE2 = 1/2 m v^2+ 1/2 I ?^2 = 1/2 m v^2 + 1/2 (1/2m R^2) v^2/ R^2 = 3 mv^2 / 4 = 3 * 2.88 * 5.76 * 5.76 / 4 = 71.66 J c), d) If the plane is frictionless then both reach the same height because they each have the same translational energy. If the plane is not frictionless then the rolling wheel reaches a greater height due to its rotational energy being expended. KE = m g h ==) h1 = KE1 / m g = 47.77 / 2.88 * 9.8 = 1.692 m and h2 = KE2 / mg = 71.66 / 2.88 * 9.8 = 2.539 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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