7 1 Visualize Solve a The weight lifter is holding the barbell in dynamic equilibrium as he stands up so the net force on the barbell and on the weight lifter must be zero The barbells have an upward contact force from the weight lifter and the gravitational force downward The weight lifter has a downward contact force from the barbells and an upward one from the surface Gravity also acts on the weight lifter b The system is the weight lifter and barbell as indicated in the figure c 7 2 Visualize Solve force on them The interaction forces between the two are equal and opposite a Both the bowling ball and the soccer ball have a normal force from the surface and gravitational b The system consists of the soccer ball and bowling ball as indicated in the figure c Assess Even though the soccer ball bounces back more than the bowling ball the forces that each exerts on the other are part of an action reaction pair and therefore have equal magnitudes Each ball s acceleration due to the which depends on the mass Since the masses of a F m forces on it is determined by Newton s second law the balls are different their accelerations are different net 7 3 Visualize Solve a Both the mountain climber and bag of supplies have a normal force from the surface on them as well as a gravitational force vertically downward The rope has gravity acting on it along with pulls on each end from the mountain climber and supply bag Both the mountain climber and supply bag also experience a frictional force with the surface of the mountain In the case of the motionless mountain climber it is static friction but the sliding supply bag experiences kinetic friction b The system consists of the mountain climber rope and bag of supplies as indicated in the figure c Assess Since the motion is along the surface it is convenient to choose the x coordinate axis along the surface The free body diagram of the rope shows pulls that are slightly off the x axis since the rope is not massless 7 4 Visualize Solve force from the Earth The push each exerts on the other is a Newton s third law force pair a The car and rabbit both experience a normal force and friction from the floor and a gravitational b The system consists of the car and stuffed rabbit as indicated in the figure c 7 5 Visualize Please refer to Figure EX7 5 Solve a Gravity acts on both blocks and where Block A is in contact with the floor there is a normal force and friction The string tension is the same on both blocks since the rope and pulley are massless and the pulley is frictionless There are two third law pairs of forces at the surface where the two blocks meet Block B pushes against Block A with a normal force while Block A has a reaction force that pushes back against Block B There is also friction between the two blocks at the surface b A string that will not stretch constrains the two blocks to accelerate at the same rate but in opposite directions Block A accelerates down the incline with the same acceleration that Block B has up the incline The system consists of the two blocks as indicated in the figure c Assess The inclined coordinate systems allow the acceleration a to be purely along the x axis This is convenient since the one component of a is zero simplifying the mathematical expression of Newton s second law 7 6 Visualize Please refer to Figure EX7 6 Solve the surface and a tension force due to the rope a For each block there is a gravitational force with the earth a normal force and kinetic friction with b The tension in the massless ropes over the frictionless pulley is the same on both blocks Block A accelerates down the incline with the same acceleration that Block B has up the incline The system consists of the two blocks as indicated in the figure c Assess The inclined coordinate systems allow the acceleration a to be purely along the x axis This is convenient since then one component of a is zero simplifying the mathematical expression of Newton s second law 7 7 Model We will model the astronaut and the chair as particles The astronaut and the chair will be denoted by A and C respectively and they are separate systems The launch pad is a part of the environment Visualize Solve a Newton s second law for the astronaut is n C on A F G on A F A y m a A A 0 N n C on A F G A m g A By Newton s third law the astronaut s force on the chair is 80 kg 9 8 m s n A on C n C on A m g A 2 7 8 10 N 2 b Newton s second law for the astronaut is n C on A F G on A F A y m a A A n C on A F G A m a A A m g a A A By Newton s third law the astronaut s force on the chair is 80 kg 9 8 m s m g A n A on C n C on A a A 2 10 m s 1 6 10 N 3 2 Assess This is a reasonable value because the astronaut s acceleration is more than g 7 8 a Visualize The upper magnet is labeled U the lower magnet L Each magnet exerts a long range magnetic force on the other Each magnet and the table exert a contact force normal force on each other In addition the table experiences a normal force due to the surface b Solve Each object is in static equilibrium with F 0 Start with the lower magnet Because U on L G L F 3 6 0 N equilibrium requires F because these are an action reaction pair Equilibrium for the upper magnet requires T on U table action reaction pairs are L on T 24 N leaving F T on L n in order for the table to be in equilibrium Summarizing For the upper magnet n and U on T n T on L 4 0 N 20 N 8 0 n T on U F n n L on U n S on T G T F U on L 8 0 N 6 0 N For the The table s gravitational force is net 4 0 N Upper magnet Table Lower magnet G U F n T on U F L on U 2 0 N 8 0 N 6 0 N G T F n U on T n L on T n S on T 20 N 8 0 N 4 0 N 24 N G L F n T on L F U on L 2 0 N 4 0 N 6 0 N 24 N n S on T …
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