1. An 9.0 m, 290 N uniform ladder rests against a smooth wall. The coefficient o

Question

1. An 9.0 m, 290 N uniform ladder rests against a smooth wall. The coefficient of static friction between the ladder and the ground is 0.55, and the ladder makes a 50.0 degree angle with the ground. How far up can the ladder can an 830 N person climb before the ladder begins to slip? ________m (answer)

2. A 220-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 37 degrees with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest? __________rad/s (answer)

3. A solid, horizontal cylinder of mass 11.0 kg and radius 1.30 m rotates with an angular speed of 8.00 rad/s about a fixed vertical axis through its center. A 0.250-kg piece of putty is dropped verticaly onto the cylinder at a point 0.900 m from the center of rotation and sticks to the cylinder. Determine the final angular speed of the system. _____________rad/s (answer)

Explanation / Answer

1) Ff=0.55*(290+830)=616 N==>

x=[616*9*sin(50)-290*9/2*sin(40)]/(830*sin(40)=6.3881 m

answer 6.4 m

2) sqrt(10*9.8*6*sin(37)/(7*0.2^2))=35.55 rad/s

answer 35.55 rad/s

3) 11/2*8*1.3^2/(11/2*1.3^2+0.25*0.9^2)=7.82943 rad/s

answer 7.83 rad/s

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