STATICS & DYNAMICS
Problem 1: Given the four concurrent forces as shown in the figure below, find the magnitude and
direction of the resultant.
Problem 2: Find the resultant of the applied forces on the beam that is loaded as shown.
Problem 2b: Find the distance of said resultant from point A
Principle: Components of Force F are:
Problem 3: Given are the concurrent forces having the following magnitudes and passing through the origin and the indicated points:
a) Compute the x-component of the resultant
b) Compute the y-component of the resultant
c) Compute the z-component of the resultant
d)Resultant Force
e) directional cosines
Concept
Problem 4:
Problem 1.
Find the resultant of the following concurrent forces passing thru the origin and the following respective points.
Problem 2. Equilibrium of Force System in Space. Find the forces in elements AB, AC, and AO. Note: O, B and C are 3D-hinged
support.
•
Concept
• A suspended cable is assumed to be parabolic when the uniformly
distributed load is assumed to be acting on a horizontal projection.
Problem 5. The cable shown supports a uniformly distributed load of 30kN/m of horizontal projection.
5a) Find the tension at the lowest point of the cable
5b:)Find the tension at the left support
5c) Find the total length of the cable ends and total length of
Concept
• A suspended cable is assumed to be A CATENARY when the uniformly
distributed load is assumed to be acting ALONG THE LENGTH OF THE
CABLE
Problem 3: Catenary Cable. An 800 m cable weighing 30 N/m is supported at the ends that are 100m vertically apart, the
lowest point is 20m lower than the lower support.
A) Find the tension at supports
b) Find the distance between supports.
Concept
• If the weight of the cable is negligible, the horizontal component of
tension at any point of the cable is constant.
M=Hy
M= moment at any point of the cable due to vertical forces
left/right of the said point
H=horizontal component of tension at any point of the cable
y=vertical distance between line connecting the supports and the
point considered
Problem 7: CE board Exam
for the cable loaded as shown in figure ME06-02
Problem 4. A 100 kg block shown is acted upon by horizontal force P.
a) Find P for motion to impend upward.
b) Find the P to prevent motion. Note u=0.1
Problem 5. In the figure shown below, u=0.3 for all contact surface. Ma=150 kg, Mb=200 kg
a) If theta=0, find P for motion to impend to the right.
b) If theta=0, find P to just prevent the motion
Problem 6. Block A is 200 kg & us=0.2 Find the mass of block B so that motion impends to the
a) Right
b) Left if u=01
Problem 7. Find theta for motion to impend ma=150 kg, mb=200 kg, u=0.3
Problem 8. Find P for impending motion.
Ma=150 kg, mb=200 kg, u1=0.1, u2=0.3
Problem 1: A motorist is travelling at 70km/hr when he sees a traffic light in an intersection 250 m ahead turn red. The light’s
red cycle is 15 s. The motorist wants to enter the intersection without stopping his vehicle, just as the light turns green.
1.1 What uniform deceleration of the vehicle will just put the motorist in the intersection when the light turns green?
0.18m/s2,0.37m/s2, 0.25m/s2, 1.3m/s2
1.2 If the vehicle decelerated at a constant rate of 0.5m/s2, what will be its speed when the light turns green? 43, 59, 52, 63
kph
Problem 2. A body is uniformly accelerating from zero to 1.8m/s2 at 4 sec. If its initial velocity is 3m/s, find the
distance traveled after 4 seconds. 16.8m,18.4m,15.5m,19.2m
Problem 3. An object moves along a path whose parametric equations are y=2t2 and x=t3 where x and y are
distances traveled in meter and t is time in second. Compute the acceleration after 3 seconds.
18.44m/s2,,12.45m/s2,15.67m/s2,13.23m/s2
Problem 4. A car travels at initial velocity of 11m/min the first minute and accelerate at the rate of (a=2+2t^2)
where a is in m/min2 and t is in minutes. Compute the velocity of the car when t=2 minutes.
31m/min,35m/min,25m/min,18m/min
Problem 5. If x=t3 and y=2t2,where x and y are in meters and t in seconds, find the velocity at t=2seconds.
13.04m/s.15.38,14.42,16.84
A stone is thrown fron the top of a building 50 m high. The initial velocity is 200m/s and released at an angle of
60 degrees from horizontal. Assume wind is moving horizontal. Assume wind is moving horizontally with a speed
of 5m/s.
6.1. Compute the time for the stone to reach the maximum height. 17.66 sec, 15.23 sc, 19.65 sec, 12.32 sec
6.2 Compute the maximum height above the ground.1579.14m, 1621.14m,1435.14m,1765.14m
Problem 7. A projectile is fired at an initial slope of 4 vertical to 3 horizontal. It reached the max. height 8m away
from the origin and hits the ground that is 2m below the origin.
7.1 Calculate the initial velocity. 11.79m/s,10.18m/s,12.78m/s,13.45m/s
7.2. Find the maximum height reached by the said projectile.5.33m/s,6.12m/s,4.78m/s,5.13m/s
7.3. Find the range of the same. 20.11m,6.27m,19.62m,17.39m
Problem 8. A particle moves on a circular path of radius 2.5m. Compute the normal acceleration if the angular
speed is 10 rad/min. 0.089m/s2,0.059m/s2,0.071m/s2,0.092m/s2
A car enters point A of the semi circular track shown at 120 kph and leaves point C at 180 kph. If it gains speed at
uniform rate, and radius of track is 300m, find the following:
9.1 Velocity of car as it passes point B. 41.67m/s,33.58,25.13,42.94
9.2 Tangential acceleration of car as it passes point B. 0.71, 0.73,0.73,0.66m/s2
9.3 Acceleration of the car as it passes point B. 4.83 m/s2,5.83m/s2, 6.06m/s2,4.44m/s2
Problem 10: From the figure shown, car A has a velocity of 65 kph traveling at a constant acceleration of 1.5
m/s2. At the same time, car B is travelling at a constant velocity of 75 kph.
10.1 Determine the velocity of a car B relative to a passenger at A. 14.61m/s,17.37,17.25,19.59
10.2 Determine the acceleration of car B along the curve path.1.35m/s2,1,79m/s2,2.17m/s2,1.52m/s2,
10.3 Determine the relative acceleration of car B with respect to a passenger at car A.
0.87m/s2,9,79m/s2,1.94m/s2,1.15m/s2,
Problem 12.A block moving at 22 m/s stops after travelling 100 m on a horizontal surface. Compute the
coefficient of kinetic friction between the block and ground surface. 0.22,0.28,0.78,0.25
Problem 13. The 5kg slider is released from rest at point A and slides with negligible friction in a vertical plane
along the circular rod. The attached spring has a stiffness of 480N/m and an unstretched length of 0.75m.
13.1 Compute the change in potential energy when the slider is at B in joules. 36.8 J, 40.4J,27.9J,39.6J
13.2. Compute the change in elastic potential energy when the slider is at B in Joules. 103 J,128J,112J,110J
13.3 Compute the velocity of the slider at B in meter per second. 7.71 m/s,4.99m/s,6.76m/s,8.89m/s
Problem 14. As shown in the figure the block of mass m=1.6kg is placed on a horizontal plane and attached to an ideal spring.
The static and kinetic coefficients of friction between the block and the plane are given in the figure. The spring has a stiffness
of k=30N/m and is undeformed when x=0. the block is launched at x=9 with the velocity of 6m/s to the right.
14.1 Compute the value of x when the block first comes to rest. 1.28m,1.15m,1.41m,1.49m
14.2 Compute the force that tends to move the block to the left when the block comes first to rest.
38.49N,34.76N,38.55N,39.27N
14.3 Compute the speed of the block when it reaches x=0 for the second time. 5.43m/s,4.51m/s,5.29m/s,5.07m/s