A block of mass M = 20 kg rides on a frictionless horizontal plane surface which we choose to describe as the xy-plane. The z-direction is vertical, perpendicular to the xy-plane, with positive z pointing upward. At t = 0 , two constant applied forces, →F1 = 8 , 4 , 10 N and →F2 = 12 , 6 , 10 N suddenly begin to act. Take g = 10 m/s 2 for the weight force. (a) (i) Draw a free-body diagram, looking edge on to the plane, showing clearly the forces which act on the block in the vertical direction. (ii) Draw a free-body diagram, looking down on the plane, showing clearly the forces which act on the block in the horizontal direction. (b) Express each of the forces acting on the block in terms of its Cartesian components (in the directions specified by x, y, and z). [Hint: If you do not know the magnitude of the vector, but you do know its direction, then use a symbol – for the time being – for the magnitude.] (c) Sum the forces to obtain the three components of the net force. (d) Apply Newton’s Second Law in each of the coordinate directions separately. (z) Consider the vertical direction. Recognise that the block’s remaining on the plane ensures that the z-component of the block’s acceleration is zero. Use this fact to ascertain the – previously unknown – magnitude of one of the forces. (y) Determine the y-component of the particle’s acceleration. (x) Determine the x-component of the particle’s acceleration. (e) At t = 0 s the block is at rest at the origin on the surface, i.e., (0 , 0 , 0) m. Determine the position and the velocity of the particle at t = 10 s.
PHY 203 Introduction to Physics NAME:
(17.1) A block of mass M = 20 kg rides on a frictionless horizontal plane surface which
we choose to describe as the xy-plane. The z-direction is vertical, perpendicular to the
xy-plane, with positive z pointing upward. At t = 0 , two constant applied forces,
→F1 =
8 , 4 , 10
N and →F2 =
12 , 6 , 10
N
suddenly begin to act. Take g = 10 m/s
2
for the weight force.
(a) (i) Draw a free-body diagram, looking edge on to the plane, showing clearly the forces
which act on the block in the vertical direction.
(ii) Draw a free-body diagram, looking down on the plane, showing clearly the forces
which act on the block in the horizontal direction.
(b) Express each of the forces acting on the block in terms of its Cartesian components
(in the directions specified by x, y, and z). [Hint: If you do not know the magnitude of
the vector, but you do know its direction, then use a symbol – for the time being – for the
magnitude.]
(c) Sum the forces to obtain the three components of the net force.
(d) Apply Newton’s Second Law in each of the coordinate directions separately.
(z) Consider the vertical direction. Recognise that the block’s remaining on the
plane ensures that the z-component of the block’s acceleration is zero. Use this fact to
ascertain the – previously unknown – magnitude of one of the forces.
(y) Determine the y-component of the particle’s acceleration.
(x) Determine the x-component of the particle’s acceleration.
(e) At t = 0 s the block is at rest at the origin on the surface, i.e., (0 , 0 , 0) m. Determine
the position and the velocity of the particle at t = 10 s.
Fall 2021 Section: 01 02 Problem Set #17
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