Engineering Mathematics
Problem 1
The truck shown in Figure P-1 moves from rest with constant acceleration ˙a up an incline of angle q. Find the greatest speed v that the truck can acquire in a distance d, if the crate C is not to slip on the truck bed. The coefficient of static friction is m.
Problem 2
In Figure P-2 a horizontal force ˙Fa of magnitude
20N is applied on the block as it slides a distance of d = 0.5m up a frictionless ramp. Then,
(a) During the displacement, find the net work done by ˙Fa, the gravitational force and the normal force ˙N on the block.
(b) If the block has zero kinetic energy at the start, find the speed at the end of the displacement
Problem 3
Masses m2 and m3 are initially at rest and the spring of length â„“0 is unstressed. Then mass m1, traveling with velocity v0 in a direction perpendicular to the spring, hits m2 inelastically and sticks to it. In the ensuing motion the spring stretches to a maximum length 3â„“0 Solve for v0, assuming that the masses are equal and can be considered as particles.
Problem 4
Consider the conservative for
Figure P-2
Figure P-3
Ë™F = (2 z2 cosh x − y2)Ë™i + 2 y (z − x)Ë™j + (4 z sinh x + y2)Ë™k
(a) Find the corresponding potential energy function.
(b) Find the work done by ˙F in moving a particle from the origin along the path y = sin(p x/2)
to the point (2, 0, 0).
Problem 5
A collar of mass m slides without friction along a circular track of radius R as shown in Figure P-5. Attached to the collar is a linear spring with spring constant K and unstretched length zero. The spring is attached at the fixed point A located a distance 2R from the center of the circle. Assuming no gravity
and the initial conditions q(t = 0) = q0 and qË™ (t =
0) = q˙0, determine
(a) the differential equation of motion for the col- lar in terms the angle q
(b) the reaction force exerted by the track on the collar as a function of the angle q
Problem 6
A star camera on a satellite observes three stars. The directions of the stars in the camera S frame are given by the unit vectors
S˙s1=
0.036103
−0.20475
S˙s2 =
0.088521
0.24321
S˙s3 =
−0.32139
−0.11698
 0.9781
 0.9659 
 0.9396 
The astronomical star catalog lists the coordinates of the same stars in the inertial frame N as
N ˙s1 =
−0.34066
N ˙s2 =
−0.05727
N ˙s3 =
−0.57125
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Engineering Mathematics
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Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet.
Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Hac habitasse platea dictumst vestibulum rhoncus est pellentesque. Amet dictum sit amet justo donec enim diam vulputate ut. Neque convallis a cras semper auctor neque vitae. Elit at imperdiet dui accumsan. Nisl condimentum id venenatis a condimentum vitae sapien pellentesque. Imperdiet massa tincidunt nunc pulvinar sapien et ligula. Malesuada fames ac turpis egestas maecenas pharetra convallis posuere. Et ultrices neque ornare aenean euismod. Suscipit tellus mauris a diam maecenas sed enim. Potenti nullam ac tortor vitae purus faucibus ornare. Morbi tristique senectus et netus et malesuada. Morbi tristique senectus et netus et malesuada. Tellus pellentesque eu tincidunt tortor aliquam. Sit amet purus gravida quis blandit. Nec feugiat in fermentum posuere urna. Vel orci porta non pulvinar neque laoreet suspendisse interdum. Ultricies tristique nulla aliquet enim tortor at auctor urna. Orci sagittis eu volutpat odio facilisis mauris sit amet.
Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.
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