Solution: (a)The second law force diagrams of two mass are shown in figure (b) Assume that the system does not move, so we have m=H,M=0.2×50=10(kg) ∫,=0 f=MgH2=50×9.8×0.2=980(N f= Nu 10×9.8=980(N) IMg-N=0 (c)If m=m=5kg, assume the system does not move,then T=0 f T=f 10×9.8=49.0(N) As the maximum static friction force fm=Mg2=50×9.8×0.2=980(N) From the above, we know T<f Thus the magnitude of the frictional force on the 50 kg block is 49N. The system does not move, so the friction force is a static friction force 2. In the system shown in Fig 4, a block(of mass m=9.5kg)slides on a frictionless plane inclined at an angle 6=34. The block is attached by a string to a second block(of mass m2=2. 6kg). The system is released from rest. (a) Find the acceleration and the tension in the string. (b)If taking into account a frictional force between Fig 4 block I and the plane, what is the acceleration of the tension in the string? Use the values 八=0.24and=0.15Solution: (a) The second law force diagrams of two mass are shown in figure. (b) Assume that the system does not move, so we have ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ − = = − = − = 0 0 0 Mg N f N T f mg T s s s µ ⎪ ⎩ ⎪ ⎨ ⎧ = = = × = = = × × = = = × = ⇒ 10 9.8 98.0(N) 50 9.8 0.2 98.0(N) 0.2 50 10(kg) or f T mg f Mg m M s s s s µ µ (c) If 5kg 2 1 m′ = m = , assume the system does not move, then ⎩ ⎨ ⎧ − ′ = ′ − = 0 0 s T f m g T 10 9.8 49.0 (N) 2 1 2 1 ⇒ T = fs ′ = mg = × × = As the maximum static friction force is 50 9.8 0.2 98.0(N) fs max = Mgµ s = × × = From the above, we know s max T < f Thus the magnitude of the frictional force on the 50 kg block is 49N. The system does not move, so the friction force is a static friction force. 2. In the system shown in Fig.4, a block (of mass m1=9.5kg) slides on a frictionless plane inclined at an angle o θ = 34 . The block is attached by a string to a second block (of mass m2=2.6kg). The system is released from rest. (a) Find the acceleration and the tension in the string. (b) If taking into account a frictional force between block 1 and the plane, what is the acceleration of the tension in the string? Use the values µs=0.24 and µk=0.15 N v Mg v T v mg v x y T v f v m1 Fig.4 m2 o 34