Assignment for Engineering Mechanics

1) The hydraulic cylinder operates the toggle which

closes the vertical gate against the pressure of fresh

water on the opposite side. The gate is rectangular

with a horizontal width of 2m perpendicular to the

paper. For a depth h = 3m of water, calculate the

required force exerted by the hydraulic cylinder to

keep the gate just closed.

2) As shown in Fig, the uniform

slender 10-lb rod AB is supported by a ball-

and-socket joint at A and leans against

both the rod CD and the vertical wall.

Neglecting the effects of friction,

determine (a) the force which rod CD

exerts on AB, (b) the reactions at B.

3) For the given loading, determine the zero-force

members in the truss shown.

4) Verify that the loaded truss is partially constrained

and indicate an alternative way to properly

constraint the truss by the addition of one or more

members.

5) A light flexible cord DABC is passed around the

circular disk of mass m and ends in a small mass-less,

frictionless pulley at C that is free to find its

equilibrium position on the cord. The coefficient of

friction between the cord and the disk is μ = 0.5. Show

that, for the position where the disk is on the verge of

turning under the action of a couple M applied to the

disk, the angle (BOA) between the normals (OB and

OA) to the cord at the tangency points (B and A) is

equal to α = 87.3o. (8 marks)

6) For the mechanism shown, the spring of

stiffness k has an un-stretched length of

essentially zero, and the larger link has a

mass m with mass center at B. The mass of

the smaller link is negligible. Determine the

equilibrium angle θ for a given downward

force P. Use principle of minimum potential

energy only.

7) Consider a uniform square plate ABCD of mass

M hinged about point A (shown in the figure).

The plate is maintained in equilibrium in the

position shown with the help of a spring EB of

spring constant k. Obtain the frequency of

vibration of the plate for small rotation θ about

point A with respect to the equilibrium

position. What is the maximum possible value

of M for which the plate with undergo a simple harmonic motion

8) For the pruning shears shown, determine the force Q applied to the circular branch of 15-

mm diameter for a gripping force P = 200 N. (Suggestion: First draw a free-body diagram of

the isolated branch).

9) The three identical rollers are stacked on a horizontal surface as shown. If the coefficient of

static friction µs is the same for all pairs of contacting surfaces, find the minimum value of µs

for which the rollers will not slip.

10) The ball is released from position A with a velocity of 3 m/s and swings in a vertical plane. At

the bottom position, the cord strikes the fixed bar at B, and the ball continues to swing in

the dashed arc. Calculate the velocity vc of the ball as it passes position C.

11) Two barges, each with a mass of 500 Mg, are loosely moored in calm water. A stunt driver starts his 1500-kg car from rest at A, drives along the deck, and leaves the end of the 15 degrees ramp at a speed of 50 km/h relative to the barge and ramp. The driver successfully jumps the gap and brings his car to rest relative to barge 2 at B. Calculate the velocity v2 imparted to barge 2 just after the car has come to rest on the barge. Neglect the resistance of the water to motion at the low velocities involved.

12) Motion of the roller A against its restraining spring

is controlled by the downward motion of the

plunger E. For an interval of motion the velocity of

E is v = 0.2m/s. Determine the velocity of A when θ

becomes 90 degrees.

13) The uniform slender bar of mass m and length L with small end rollers is released from rest

in the position shown with the lower roller in contact with the horizontal plane. Determine

the normal force N under the lower roller and the angular acceleration α of the bar

immediately after release.