A high school physics instructor catches one of his students chewing gum in class. He decides to discipline the student by asking that he stick the gum to a fan and calculate how fast the fan is moving when the gum gets thrown off. The label says that the diameter of the fan is d = 29 cm, and at full speed it turns at a rate of f = 35 rev/s, and that the fan is guaranteed to accelerate uniformly. The fan takes t = 11 s to go from rest to full speed.

(a) Find the angular speed alpha
(b) Find the tangential components of the acceleration as the fan is speeding up
(c) What is the magnitude of centripetal acceleration as the fan is turning at top speed.
(d) Find the tangential components of the acceleration of the gu. When the fan is at full speed.

Part f - example: finding two forces (part i) two dimensional dynamics often involves solving for two unknown quantities in two separate equations describing the total force. the block in (figure 1) has a mass m=10kg and is being pulled by a force f on a table with coefficient of static friction îľs=0.3. four forces act on it: the applied force f (directed î¸=30â above the horizontal). the force of gravity fg=mg (directly down, where g=9.8m/s2). the normal force n (directly up). the force of static friction fs (directly left, opposing any potential motion). if we want to find the size of the force necessary to just barely overcome static friction (in which case fs=îľsn), we use the condition that the sum of the forces in both directions must be 0. using some basic trigonometry, we can write this condition out for the forces in both the horizontal and vertical directions, respectively, as: fcosî¸â’îľsn=0 fsinî¸+nâ’mg=0 in order to find the magnitude of force f, we have to solve a system of two equations with both f and the normal force n unknown. use the methods we have learned to find an expression for f in terms of m, g, î¸, and îľs (no n).

Agroup of students is studying convection currents. they fill two identical balloons with the same amount of helium. one balloon is placed in a freezer and the other in an area with warm air. after 10 minutes, the balloons are released from a height of 1 meter. which of the following do the students most likely observe? question 2 options: the balloons rise at the same rate. both balloons are the same size. the ballons both rise. the cold ballon is larger than the warm balloon. the cold balloon expands and rises. the warm balloon shrinks and sinks. the warm balloon expands and rises. the cold balloon shrinks and sinks.

Amira pulls a 3 pound wagon 4 feet. how much work has she done?