SPME425

HOMEWORK #4 - LINEAR KINETICS

 

The sketch shows a diver at the instant of contact with the board (TD) and at the instant of takeoff (TO). 

• The time between the instants of TD and TO is 0.40 s. 

• The mass of the diver is 70 kg. 

• The location of the center of gravity (c.g.) of the diver at TD is:     s_TD = (1.00 i + 11.00 j) m

• The velocity of his c.g. at TD is:        v_TD = (4.0 i - 1.0 j) m/s 

• Assume that the force exerted by the board on the diver between the instants of TD and TO is constant and equal to:

        F = (-500 i + 1000 j) N

• Notice in the sketch that the surface of the water will have a Y coordinate value of 0.

1.  Draw the free-body diagram of the diver at any time between the instants of touchdown (TD) and takeoff (TO).

 

2.  Draw the free-body diagram of the diver at any time while he is airborne.

 

3.  From the information given, compute the following measures:

        a.  the net impulse exerted on the diver between the instants of TD and TO, in both the X and Y directions.

        b.  the initial linear momentum of the diver at the instant of TD, in both the X and Y directions.

        c.  the linear acceleration of the diver between the instants of TD and TO, in both the X and Y directions.

 

4.  From the information given and your answers to number 3, compute the following measures:

        a.  the location of the c.g. of the diver at the instant of TO.

        b.  the velocity of the c.g. of the diver at the instant of TO.

        c.  the takeoff angle of the diver - the angle between the horizontal plane and the tangent to the trajectory of the c.g. at takeoff).

5.  Using your answers to number 4, compute the following measures:

        a.  the location of the diver's c.g. when it enters the water.

        b.  the velocity of the divers c.g. when it enters the water.

        c.  the vertical velocity of the c.g. at its peak.

        d.  the horizontal velocity of the c.g. at its peak.

 

6.  What was the linear acceleration of the c.g. between the instant of TO and the instant when the diver entered the water

        a.   in the X direction

        b.   in the Y direction