Quiz#3.

Q1.      A ball is thrown at an angle of 60⁰ above the horizontal and with an initial speed of 20.0 m/s.  It hits a building 8 m away at a point H meters above the ground.

                x =  v_o cosq_o t

            Therefore,  8 = 20 cos 60^o t      Þ   t  = 0.8 s

            (b) Find the value of H.

         y  =  v_o sin q_o t  - (1/2) g t²  Þ  H = 20 sin 60^o *0.8  - (1/2) * 9.8* (0.8)²

                                 \ H = 10.7 m

Q2.      A block of mass M = 10.0 kg on a rough inclined plane ( q = 30^o ) is connected by a light string that passes over a frictionless pulley to a hanging steel ball of mass m , as shown in the figure. The coefficient of kinetic friction between the block and the surface is 0.20 . The acceleration of the block down the incline is 1.20 m/s².  Find

(a) the tension in the string, and

(a)        M g sinq  - T – m M g cos q  = M a     

            Þ  T = M g (sinq   - m cos q  ) - M a

                 T  = 10 * 9.8 ( sin 30 – 0.2 cos 30 ) – 10 *1.2

        T = 20.0 N

(b)        m g  - T  = m a            

        Þ        m  = T / ( g + a)    Þ  m = 20/ ( 9.8 +1.2)  kg

                            Hence   m = 1.82 kg.

Q3.      A 2000-kg car passes over a bump in a road that follows the arc of a circle of radius R = 50 m, as shown in the Figure.  What is the maximum speed the car can have as it passes the highest point before losing contact with the road?

            (Show the forces acting on the car in the vertical direction, then apply Newton’s law)

Solution:

            m g  -  N = m a_r   , where a_r  =  v² / R

            the normal force  is zero.  Hence, when N=0, v = v _max

             Therefore, m g = m v_max² / R 

           Hence, v_max =  Ö(g R)   = Ö(9.8 * 50) m/s =  22.1 m/s