Question

Your engineering team has been assigned the task of measuring the properties of a new jet-engine turbine. You have previously determined that the turbine's moment of rings. Your plan is to run the turbine up to a predetermined rotation speed o, cut the pow and measure the time At taken for the turbine to reduce its rotation speed by 50%. The data you have gathered is in the table below. At (s) (rpm) 1500 19 22 1800 2100 25 2400 30 2700 34 (a) Use Newton's second law to write an expression for the frictional torque t. and the frictional (b) (iWrite a sentence justifying why the initial rotation speed must have opposite signs torque takes to reduce the turbine's rotation speed by 50 % is (ii) Show that the time At= (c) Convert the values of o in the table to units of rad s. (d) Draw an appropriate graph of the data, estimate its slope and use your estimate to determine the frictional torque r. Remember to label the axes of your graph. A solid sphere is released from rest at the top c the horizontal. The sphere rolls a distance L down the slope without slipping. The an incline, which is at an angle e to sphere and R is the radius of the sphere. The gravitational acceleration is g. You can assume no energy is lost due to dissipative forces ol ad e in the sphere's potential energy as it (b) Write down an expression for the sphere's total kinetic energy after rolling through the distance L as in the diagram (c) Show that the sphere's final speed is: 10 gL sin (d) Derive an expression for the acceleration of the sphere aphr in terms of and (e) Express the acceleration of a point particle aparticle Sliding down the same incline from rest in terms of and e. (f) Compare ahere and aartic le (e.g. ><) and briefly explain why they are different.

Answer 1

() Lsino fotenbry cmery in kimehr Eneyy (b) Tromslationa Energy +Rotation Enery KE = 2 2 for sphere 2 2 mR / 2 T R KE 2 2 2 KE 10

Conservation of Enery AU KE dino 1 l0 -f- F- ma Ouie 2 mR 2 fR R 2ma in af 2 ma ma ES

a ccefer stetey deJuag Accelcrahon of So sphore atrele