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# Problem 1

The truck shown in Figure P-1 moves from rest with constant acceleration Ë™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  Ë™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 Ë™Fa, the gravitational force and the normal force Ë™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 Ë™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) = qand qË™ (t  =

0) = qË™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

SË™s1=

0.036103

0.20475

SË™s2 =

0.088521

 3

0.24321

SË™s3 =

0.32139

 9

0.11698

 5

ï£°  0.9781

ï£° 0.9659  ï£»

ï£°   0.9396 ï£»

The astronomical star catalog lists the coordinates of the same stars in the inertial frame N as

0.5591

0.27356

0.27022

 5

 2

N Ë™s1 =

0.34066

N Ë™s2 =

0.05727

N Ë™s3 =

0.57125

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### Engineering Mathematics

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## More Engineering Mathematics: Questions & Answers

Q

### Human Resource Management & Talent Developmen

Strategic planning in HR is about using technological tools and working with people. This assignment will allow you to think about both areas. Use your module readings, the Argosy University online library resources, and the Internet to research HR challenges in relation to people and technology ...

Q

### Php report

Use the OWASP top 10 security threats to review the security features available in PHP and ASP.NET. You should critically analyse PHPâ€™s ability to counter each of the top 10 threats (approx. 2000 words). Your report should have an introduction, a main body and conclusion. It should focus o ...

Q

### SWOT Analysis

Maximillian Lazlo (known as “Max” or "86" to his friends) was the marketing manager for Lazlo Vitamins Pty Ltd. Lazlo made a variety of vitamins and nutritional supplements that it sold to retailers throughout South Australia. Lazlo had been established in Adelaide in 1986 by Max's fa ...

Q

### Nursing Case study

though The Subject is Nursing this Case study is related to Bioscience. Before you start to write read the attached files carefully. About references: are provided by Universities . No need to find out other references. need to go through all the provided resources before start to write. Word count ...

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