1) A fan's blades accelerate from 250 rpm to 350 rpm over 5.75 seconds. The angular acceleration is calculated as well as the number of revolutions during acceleration. 2) A pebble on an accelerating disk experiences centripetal force due to the disk's motion. The maximum force and speed before slipping are calculated, as well as the time to reach this speed. 3) The position of a counterweight on a seesaw is calculated to balance different masses on the meterstick. 4) The maximum position a painter can stand on a board overhanging a scaffold is calculated to prevent tipping. 5) The linear speed of a rolling hoop leaving an inclined plane

1. 1) (6 points) The blades of a fan running at low speed turn at 250 rpm. When the fan is
switched to high speed, the rotation rate increases uniformly to 350 rpm in 5.75 s.
(a) What is the magnitude of the angular acceleration of the blades in rad/s2
?
(b) How many revolutions do the blades go through while the fan is accelerating?
2) (6 points) A horizontal disk of radius 5.00 cm accelerates angularly from rest with an
angular acceleration of 0.250 rad/s2
. A small pebble located halfway out from the center
has a coefficient of static friction with the disk of 0.15.
(a) What is the maximum centripetal force that can be supplied to the pebble?
(b) How fast can the pebble go before it starts to slip? (units must be in rad/s)
(c) How long will it take for it to get up to this speed?

2. 3) (4 points) A uniform meterstick pivoted at its center has a 100-g mass suspended at the
25.0-cm position.
(a) At what position should a 75.0-g mass be suspended to put the system in equilibrium?
(b) What mass would have to be suspended at the 90.0-cm position for the system to be
in equilibrium?
4) (3 points) While standing on a long board resting on a scaffold, a 70-kg painter paints the
side of a house, as shown. If the mass of the board is 15 kg, how close to the end can the
painter stand without tipping the board over?

3. 5) (5 points) A hoop (I=mr2
) starts from rest at a height of 1.2 m above the base of an
inclined plane and rolls down under the influence of gravity. What is the linear speed of
the hoop’s center of mass just as the hoop leaves the incline and rolls onto a horizontal
surface?
6) (9 points) For the system shown in, m1 = 8.0 kg, m2 = 3.0 kg, θ = 30°, and the radius and
the mass of the pulley are 0.10 m and 0.20 kg, respectively. I = ½ mr2
(a) What is the acceleration of the masses? (Neglect friction and the string’s mass.)
(b) What is the tension in T1 and T2?

4. 7) (5 points) The velocity of a vertically oscillating mass-spring system is given by
v = (0.750 m/s) sin(4t). Determine
(a) the frequency
(b) maximum velocity
(c) maximum acceleration
(d) period
(e) the amplitude

5. 8) (6 points) In a common laboratory experiment on standing waves, the waves are
produced in a stretched string by an electrical vibrator that oscillates at 60 Hz. The string
runs over a pulley, and a hanger is suspended from the end. The tension in the string is
varied by adding weights to the hanger. If the active length of the string (the part that
vibrates) is 1.5 m and this length of the string has a mass of 0.10 g, what masses must be
suspended to produce the first four harmonics in that length? (There are four answers)

6. 9) (18 points) Kelly the geologist is in Querretaro, Mexico searching for some prized fire
opal. Her destination is deep in an area surrounded by deep ravines and dense jungles. As
she approaches her main destination, she comes across a deep ravine. She was planning
on this as she packed a 3.8 m portable telescoping extension ladder. It has a mass of 15
kg. She was told that in order to get to her mining spot, she must get across this 2 m gap.
(a) What angle will the ladder make with the
horizontal? Round to the nearest whole number.
(b) Now since she has carefully lowered the ladder down to the bottom, she isn't entirely
sure if it will hold. She knows her mass is 48 kg. First we need to find the normal force
due to the vertical wall. What will it be? Round to the nearest whole number. Assume the
vertical wall is frictionless.
(c) Using the normal force you just found, determine the force of friction between the
ladder and the horizontal surface and compare it to the maximum allowed friction force
between the ladder and horizontal surface. The coefficient of static friction is 0.75. Can
she make it?
(d) If you answered yes, what will happen to the friction force as she climbs down the
ladder? If you answered no, would it make a difference if there was friction between the
ladder and the vertical wall?

7. Now since she has made it to her digging spot, she notices a better spot across another
ravine. At first she is disappointed that she can not make it across but then she notices
some vines hanging over the ravine. To her luck, a strong breeze blows some of the vines
toward her and she is able to grab one. She tugs on to see if it can support her weight and
it appears so. The vine appears to make a 10° angle with the vertical. She is curious to
how long the ravine is so she can make a map of the region later on.
(e) Based on the location of the vine, which is right
over the middle of the ravine, how wide is the
ravine in terms of L?
(f) What she decides to do is tie a rock to the end of the vine and release it like it's a
pendulum. She decides she is going to time the swing to determine the period of the
pendulum and from that she could figure out the length of the vine. She counts 10 swings
in 48.17 s. How long is the vine and how wide is the ravine?
(g) This is it: she has determined the width of the ravine and decides to swing across with
out a running start. However, she forgot one thing, centripetal force. It might support her
weight, but the vine might not be strong enough to support the swing. What Kelly doesn't
know is the vine can only support a tension force of 480 N before it breaks. Will she
make it to the other side or fall into the ravine. Prove your answer by finding the
maximum tension in the vine. (Hint: you need to use centripetal force)