Physics 103, Spring 2003, U.Wisconsin Example 4 T1 T=24 N M2 = 4 kg M1 = 2 kg Find acceleration of blocks and tension T1 Note friction is not specified, only external force T pulls blocks Acceleration, a = Fnet / M = T / (M1+M2) = 24 / 6 m/s2 = 4 m/s2 Tension, T1, is causing block M2 to accelerate at 4 m/s2 T1 = M2a = 4 * 4 N = 16 N 9/22/2018 Physics 103, Spring 2003, U.Wisconsin

Example 5 T1 T=24 N M2 = 2 kg M1 = 4 kg Turn blocks around…. Find acceleration of blocks and tension T1 Answers: a= 4 m/s2 (the same) and T1= M2a = 8 N (smaller) 9/22/2018 Physics 103, Spring 2003, U.Wisconsin

Example 7 s M1 M2 a Find maximum acceleration such that upper block does not slip M1 is fixed with respect to M2 - therefore, static frictional force on M1 at the M1-M2 contact surface is, f = s M1 g Answers: a= f/M1 = sg 9/22/2018 Physics 103, Spring 2003, U.Wisconsin

Example 6 mg cos () mg sin ()   Find acceleration and normal force Choose axis and calculate components Answers: a= g sin() FN=mg cos () 9/22/2018 Physics 103, Spring 2003, U.Wisconsin

Physics 103, Spring 2003, U.Wisconsin Example 8 What force does a trampoline have to apply to a 45 kg gymnast to accelerate her up at 7.5 m/s2? mg Ft 9/22/2018 Physics 103, Spring 2003, U.Wisconsin

Physics 103, Spring 2003, U.Wisconsin Example 9 A flea jumps by exerting a force of 1.2 x 10-5 N straight down on the ground. A breeze blowing on the flea parallel to ground exerts a force of 0.5 x 10 -6 N on the flea. Find the direction and magnitude of the acceleration of the flea if its mass is 6 x 10 -7 kg. mg F f 9/22/2018 Physics 103, Spring 2003, U.Wisconsin

Physics 103, Spring 2003, U.Wisconsin Example 10 mwoodOnWood= 0.5,0.3 Suppose you have a 120 kg wooden crate resting on a wood floor. (a) What maximum force can you exert horizontally on the crate without moving it? What kind of friction is impeding movement? static kinetic mg N F fk (b) If you continue to exert this force once the crate starts to slip what will its acceleration be? What is the net force acting on the crate? Force exerted Force exerted - Static friction Force exerted - Kinetic friction 9/22/2018 Physics 103, Spring 2003, U.Wisconsin

Physics 103, Spring 2003, U.Wisconsin Example 13 A contestant in a winter games event pushes a 45 kg block of ice across a frozen lake. Calculate the minimum force, F, he must exert to get the bock moving. What is the force, F’, he needs to exert if he were to pull the bock with a rope over his shoulder at the same angle above the horizontal? Is F = F’? 1) Yes 2) No 25o F cos25o F’ cos25o -F sin25o F’ sin25o F’ F ms (ice-on-ice)=0.1 9/22/2018 Physics 103, Spring 2003, U.Wisconsin

Physics 103, Spring 2003, U.Wisconsin Example 13 - Contd. F’ 25o F cos25o F’ cos25o -F sin25o F’ sin25o F ms (ice-on-ice)=0.1 N N’ Case B Case A mg mg 9/22/2018 Physics 103, Spring 2003, U.Wisconsin