CE298 Week 6 Homework solutions
1
Notes
Three states can be identified: i) the starting state (0) at A, ii) the state (1) immediately before impact at B, and iii) the state (2) immediately after impact at B. In going from from state 0 to state 1,
because
CE298 Week 5 Homework solutions
Notes
The only forces assumed to be acting are the gravitational (weight) force and the spring force, both
of which are conservative, and hence a solution in terms of potential energy is motivated.
The total potential energ
CE298 (Spring 2015) Quiz 1
Last Name: Solution Key
The double inclined plane supports two blocks A and B as
shown in the figure. Block A has a mass of 3 kg while
block B has a mass of 6 kg. A force F with a magnitude of
10 N and a direction of 70 with res
CE298 Week 3 Homework solutions
Notes
There is no need to consider the force equation in the y-direction for this particular problem.
The signs of each term in the equations and the relationship to the chosen coordinate system should
be noted.
Notes
Tw
CE298 Week 11 Homework solutions
Notes
This is a case of pure translation (the system maintains the same orientation in space, i.e., it does
not rotate about itself). As a result, the moment equation does not have a term with an angular
acceleration. Furt
CE298 (Spring 2015) Quiz 2
Solution Key
At a given instant, the bottom B of a 5-m long ladder is moving up an
inclined plane with a speed of 1.2 m/s, at which instant its speed is
decreasing at a rate of 0.1 m/s2. The plane is inclined at an angle of
15 w
CE298 (Spring 2015) Quiz 3
Solution Key
A block A of mass 60 kg rests on two identical cylindrical rollers, centered at B and C, each of radius 450
mm and mass 20 kg. The whole assembly of block and rollers moves down a plane inclined at an angle
of 15 wi
CE298S Week 2 Homework solutions
Notes
1/2
2
The radius of curvature, , is found using the formula: = 1 + ( dy / dx )
/ d 2 y / dx 2 .
Notes
The follower rod AB is constrained to move in a horizontal direction only, and hence its velocity and
acceleratio
CE298 Week 8 Homework
Notes
As each rigid body has an associated at any instant in time,
each rigid boy has an associated instantaneous center (IC) of
rotation at any instant in time. In the above, the IC for each
rigid body is therefore different at any
CE298 Week 13 Hmwk
Notes
The velocity relations (at the final state 2) are obtained from
kinematics. For example,
The method of instantaneous center of velocity might also be used to advantage here.
The total kinetic energy is the sum of the kinetic ener
CE298 Week 12 Homework
Notes
In general, the kinetic energy of rigid bodies has a contribution from both translation and rotation.
Because the crate undergoes pure translation, its contribution is purely from translation, i.e,
mC vC2 / 2 while the wheel u
Solutions to Week 1 CE298S homework
Notes:
Repeated integration is used to determine displacement from acceleration.
Notes:
For the first part, the relationship between velocity and distance (and acceleration) is used; only in
the second part, is the rela
CE298 Week 10 Homework
Notes
The above takes the (i,j,k) approach to solution; here we take the alternative approach. The general
strategy will be describe the motion of C from the point of view of the rod AB and then also from the
point of view of the r
CE298 Week 7 Homework solutions
Notes
The angular velocity, , increasing uniformly implies that the angular acceleration, =c, is constant,
hence the straightforward integration, 0 =
t
t0
c dt= c ( t t0 )= c t where t0 = 0 .
The drum is a rigid body, and
CE 298 Engineering Mechanics II: Dynamics
Homework 2
Name:
Student ID:
1.
A ball is dropped from a boat so that it strikes the surface of a lake with a speed of
3 m/s. While in the water the ball experiences an acceleration of
= 3 0.2 , where a and v are
CE 298 Engineering Mechanics II: Dynamics
Homework 1
Name:
Student ID:
1.
The vertical motion of a truck suspension system is defined by the equation
x = 2 cos 3t + 3 sin 3t + 1, where x and t are expressed in inches and seconds,
respectively. Determine t
CE 298 Engineering Mechanics II: Dynamics
Homework 5
Name:
Student ID:
1. The velocities of skiers A and B are as shown. Determine the velocity of A with respect to
B when angle = 15o.
2. Three seconds after automobile B passes through the intersection sh
CE 298 Engineering Mechanics II: Dynamics
Homework 4
Name:
Student ID:
1. An airplane used to drop water on brushfires is flying horizontally in a straight line at 150
mi/h at an altitude of 450ft. Determine the distance d at which the pilot should releas
CE 298 Engineering Mechanics II: Dynamics
Homework 6
Name:
Student ID:
1. Determine the smallest radius that should be used for a highway if the normal component
of the acceleration of a car traveling at 65 km/h is not to exceed 1.0 m/s2.
2. Racecar A is
CE 298 Engineering Mechanics II: Dynamics
Homework 9
Name:
Student ID:
1. Solve Problem 12.46 in the textbook.
2. Tilting trains, such as the American Flyer which will run from Washington to New York
and Boston, are designed to travel safely at high speed
CE 298 Engineering Mechanics II: Dynamics
Homework 10
Name:
Student ID:
1. Rod OA rotates about O in a horizontal plane. The motion of the 1.0-lb collar B is
defined by the relations r = 8 + 7 cos (t) and = 2 (3t2 8t), where r is expressed in
inches, t in
CE 298 Engineering Mechanics II: Dynamics
Homework 8
Name:
Student ID:
1. Each of the systems shown is initially at rest. Neglecting axle friction and the masses of
the pulleys, determine for each system (a) the acceleration of block A, (b) the velocity o
CE 298 Engineering Mechanics II: Dynamics
Homework 7
Name:
Student ID:
1. Solve Problem 11.161 in the textbook.
2. In anticipation of a long 7 upgrade, a bus driver accelerates at a constant rate of 2 ft/s2
while still on a level section of the highway. K
CE 298 Engineering Mechanics II: Dynamics
Homework 3
1.
Name:
Student ID:
In a boat race, boat A is leading boat B by 50 m and both boats are traveling at a
constant speed of 100 km/h. At t = 0, the boats accelerate at constant rates.
Knowing that when B