Download Force 1

Force 1
1) Two forces act on a block of mass m, as shown in the figure. The horizontal force has
a known magnitude F1, while the second force has an unknown magnitude, and the angle
 is unknown. Knowing that the acceleration of the block has a magnitude a, and is
directed at a known angle  as shown in the figure, derive an algebraic expression for the
magnitude F2 of the second force, and for the angle .
F1
F2


a
2) A fisherman catches a fish of mass m initially moving with velocity v0 away from the
fisherman. The fish is brought to rest (and eventually captured) at a distance D from the
starting point. Derive an algebraic expression for the tension in the fishing line, assuming
the deceleration to be constant.
3) Four blocks are tied together by a series of ropes, and pulled by a horizontal force on a
frictionless plane, as shown in the figure. Knowing the masses m1, m2, and m4, the
magnitude F of the pulling force, and the magnitude T of the tension between blocks # 2
and #3, derive an algebraic expression for:
a) The mass m3 of block #3.
b) The acceleration of the blocks.
c) The magnitudes of the tensions in the other ropes.
4
3
T
2
1
F
4) A block of mass m is pulled by a force of magnitude F forming an angle  with the
horizontal. Assuming the block to move horizontally, and the plane to be frictionless,
derive an algebraic expression for its acceleration. For which value of the angle  will the
acceleration be at a maximum? At a minimum?