Physics 298

Sample Test 2

1)      A missile, mass (2/9) kg, is projected at an angle of 670 with the surface of the earth (assumed
         horizontal), with a speed of 65 m/s.

   (a)     What is the horizontal component of the missile's velocity when it reaches its maximum

            height ? Ignore air resistance. (tan67 = 12/5)                                                                          (3)

 

   (b)    Use conservation of energy to determine the maximum height reached by the missile. Ignore

            air resistance. (g = 10 m/s2)                                                                                                     (6)

 

   (c)     When it reaches its maximum height the missile explodes, breaking into two equal mass
            fragments. One fragment is observed to move horizontally, to the left (see above), with a
            velocity equal to twice that of the horizontal component of the original missile immediately

            before the explosion. Determine the velocity of the other fragment immediately following
            the explosion.                                                                                                                          (8)

 

   (d)    How much kinetic energy is lost (or gained) in the explosion ?                                             (6)

   (e)     Would you classify the explosion as elastic or inelastic ?                                                      (2)

Solution


2)         When suspended from a bungee cord, at rest, a 70 kg person - the "BUNGER" - increases the

            length of a 50 m cord by 25%.

   (a)     Assuming the cord obeys Hooke's Law, calculate its spring constant. (g = 10 m/s)              (5)

   (b)    Use the principle of energy conservation to determine how far the "BUNGER" will fall when
            jumping from a bridge. (Ignore air resistance)                                                             (11)

   (c)     Assuming zero air resistance how far would you expect the "BUNGER" to bounce back
            towards the bridge ?                                                                                                                (2)

   (d)    In a real situation, on the first bounce, the "BUNGER" returns to 10 m below the bridge.

            How much work is done against the resistive forces from the time the jump begins till the top
            of this first bounce ?                                                                                                               (7)

 

Solution

3)         A soccer ball of mass 1kg is moving at a speed of 8 m/s.

    (a)    What is the magnitude of the momentum of the ball ?                                                           (4)

    (b)   What is the kinetic energy of the ball ?                                                                                   (4)

    (c)    The ball strikes a brick wall and rebounds with a speed of 5 m/s. Calculate the change in

            momentum of the ball.                                                                                                (6)

    (d)   If the ball is in contact with the wall for 0.1 s, what is the magnitude of the force exerted

            by the ball on the wall ?                                                                                               (6)

    (e)    The wall remains at rest relative to the earth. Is the momentum of the system comprising
            the wall and the ball conserved ? If not, why not ?                                                                (5)

 

Solution

 

4)         The flywheel of a steam engine runs with a constant angular speed of 72 rev/min. When the
            steam is shut off, the friction of the bearings and the air brings the wheel to rest in 2 minutes.

   (a)     What is the constant angular acceleration, in rev/s, of the wheel during slowdown ?            (7)

   (b)    How many rotations does the wheel make before coming to rest ?                                       (7)

   (c)     What is the tangential component of the linear acceleration of a particle that is 10 cm from
            the axis of rotation when the flywheel is turning at 6/(Ö(2p)) rev/mi                                    (4)

 

   (d)    What is the magnitude of the net linear acceleration of the particle in (c) ?                           (7)

Solution


5)         The moment of inertia of a disc about an axis through its centre, perpendicular to its plane, is
            given by (MR2)/2, where R is the radius and M the mass.

   (a)     Use the parallel axis theorem to obtain an expression for the moment of inertia of the disc,
            about an axis perpendicular to its plane, through its edge (at B).                                           (5)

 

   (b)    A force of 30 N is applied at point A, as shown above. If the disc has a radius of 8 m,
            determine the magnitude of the torque due to this force, abut the axis through B.                (4)

   (c)     What angular acceleration does this force impart to the disc, when it rotates about the axis
            through B ? (M = 2.5 kg)                                                                                                        (4)

 

   (d)    The disk is rotating at 7 rev/min (about B), when a mass of 2.5 kg is placed on its rim, at C.
            What is the angular velocity (in rev/min) of the disc (and the mass), immediately after the

            mass is positioned on it ?                                                                                                       (8)

    (e)    What is the (linear) speed of the mass at this time ?                                                              (4)

Solution