Download 1. A 70 kg adult sits at the end of a 10 m board, on the other end of

1. A 70 kg adult sits at the end of a 10 m board, on the other end of which sits a 30 kg child.
Where should the pivot be placed so the board (ignore its weight) is balanced?
We choose the coordinate system shown, with positive torques clockwise. We write ∑ =I 
about the support point A from the force diagram for the board and people:
∑  A=−m1g  L−dm2gd=0
−30 kg10m−d70 kg d=0
 d=3.0 m from the adult.
2. A person exerts a force of 45 N on the end of a door 48cm wide. What is the magnitude of the
torque if the force is exerted
a) perpendicular to the door
=LF sin =0.84 m 45 N  sin 90o=38 m.N.
b) at a 60-degree angle to the face of the door?
o
=LF sin =0.84 m 45 N  sin 60 =33 m.N.
3. An automobile engine slows down from 4000 rpm to 1200 rpm in 3.5 s. Calculate
a) its angular acceleration
= 0 t ;
1200 rev/min2 rad /rev1min /60s=4000 reev/min2 rad /rev1 min/60s3.5 s ,
2
 =−84 rad / s
b) the total number of revolutions the engine makes in this time.
=0.5 0t ;
=0.5 4000 rev/min1200 rev/min[2 rad /rev1 min/60s]3.5s =954 rad.
 =954 rad 2 rad /rev−1=1.5×10 2 rev.