Abowling ball rolls with-out slipping up a ramp that slopes upward at an angle î² to the horizontal. treat the ball as a uniform solid sphere, ignoring the finger holes. (a) draw the free-body diagram for the ball. explain why the friction force must be directed uphill. (b) what is the acceleration of the center of mass of the ball? (c) what minimum coefficient of static friction is needed to prevent slipping?

An object with initial temperature 130 ∘ f is submerged in large tank of water whose temperature is 50 ∘ f . find a formula for f ( t ) , the temperature of the object after t minutes, if the cooling constant is k = − 0.2 . remember newton's law of cooling (the rate of change of temperature with respect to time is equal to k times the difference between the temperature of the object and the surrounding temperature) ! : )