qz6sol_6942s11

# qz6sol_6942s11 - edge E i = E f ⇒ mg(Lsin θ =(1/2)mv...

This preview shows page 1. Sign up to view the full content.

TA: Tomoyuki Nakayama Monday, March 14, 2011 PHY 2048: Physic 1, Discussion Section 6942 Quiz 6 (Homework Set #8) Name: UFID: Formula sheets are not allowed. Do not store equations in your calculator. You have to solve problems on your own; memorizing final algebraic expressions from homework assignments and just plugging numbers into them will not give you full credit. Leave all your work. ________________________________________________________________________________ In the figure, a solid uniform sphere of radius 5.00 cm and mass 2.00 kg starts from rest and rolls without slipping a distance L = 6.00 m down a roof that is inclined at angle θ = 40°. The rotational inertia of a solid sphere is I = (2/5)mr 2 . a) What is the angular speed of the cylinder about its center as it leaves the roof? When the sphere rolls down the roof, the mechanical energy of the sphere is conserved. We apply the energy conservation equation to the initial position and the edge of the roof and solve the equation for the angular speed at the
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: edge. E i = E f ⇒ mg(Lsin θ ) = (1/2)mv 2 + (1/2)I ω 2 mgLsin θ = (1/2)m(r 2 ω 2 ) + (1/2)(2/5)mr 2 ω 2 = (7/10)mr 2 ω 2 ω = √ (10gLsin θ /7r 2 ) = 147 rad/s b) The roof's edge is at height H = 5.00 m. How far horizontally from the roof's edge does the cylinder hit the level ground? After the sphere leaves the roof, it undergoes a projectile motion. The initial speed of the projectile motion is the speed of the sphere at the edge of the roof: v = r ω = 7.35 m/s At the edge, the sphere is moving at an angle of 40º below the horizontal. x and y components of the initial velocity of the projectile motion are v 0x = v =cos(-40º) = 5.63 m/s, v 0y = v sin(-40º) = -4.72 m/s When the sphere hits the ground, the vertical displacement of the sphere is –H. The flight time is -H = v 0y t – (1/2)gt 2 t = (-v 0y + √ (v 0y 2 + 2gH))/g = 0.637 s During this time interval, the horizontal displacement of the sphere is Δ x = v 0x t = 3.59 m...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern