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Answer the following questions: 1- a) How high can a man throw a ball if he can throw it with initial velocity 8 m/s (2) v 2 = vo2 − 2 g ∆ y 0 = (8) − 2(10 ) ∆ y ∆ y = 3.2 m 2 2. A speedboat increases its speed uniformly from 20 m/s to 30 m/s in a time of 5 sec. (a) Find the magnitude of its acceleration (2) v = vo + a t ⇒ 30 = 20 + a (5) ⇒ 30 = 20 + a (5) a = 2 m / s2 (b) How far does the boat travel during that time? (2) v + vo ∆x = t 2 30 + 20 ∆ x = 5 =125 m 20 B 3- From the figure, find: 70m a) The x-component of the vector B (1) B X = 70 cos120 = − 35 m b) The y-component of the vector B (1) B y = 70 sin 120 = 60.6 m c) For the vector C= A + B i) , find C X = AX + B X = 20 + (− 35) = − 15 m (2) ii) C y = Ay + B y = 60.6 + 0 = 60.6 m (2) iii) (1) The direction that C makes with the positive x axis 60.6 + 180 = − 76 + 180 =103.9° 15 θ = tan −1 − 1200 A 20 m 4- In the figure shown below, the incline is frictionless and the mass m falls with acceleration 4.0 m/s2. (Ignore the friction and the mass of pulley). If the tension in the cord connecting the two masses is T= 16 N a) Find the angle θ of the incline. Σ FX = T − m ′ g sin θ = m ′ a 16 − 2 (10) sin θ = 214 θ = 23.5° (2) 2 kg m θ b) Find the mass m of the falling body. Σ Fy = m g − T = m a T = m (g − a ) ⇒16 = m (10 − 4 ) m = 2.67 kg (2) 5- Two blocks are placed one on the top of the other as shown in the figure. A force F is applied to the lower block. If the coefficients of friction between the lower block and the surface are μ s = 0.50 and μ k = 0.25, a) What value of F is needed to put the block into motion? (2) F = f smax = µ S (m1 + m2 ) g F = 0.5 (2 + 3)10 = 25 N 2 kg F 3 kg b) If F= 20 N, what is the magnitude of the frictional force. (1) f s = F = 20 N 6- A space station of diameter 80 m is turning about its axis at a constant rate. If the acceleration of the outer rim of the station is 2.5 m/s2, a) Find the speed of the station (1) v2 ⇒ v = ar = 2.5 (40) r v = 10 m / s ar = b) What is the period of revolution of the space station? (1) v= 2π r 2 π r 2(3.14 ) 40 ⇒T = = T v 10 T = 24.8 s c) How many revolutions per minute does the station make? (1) 1 60 f= ⇒ f= = 2.4 rpm 24.8 T