I need help in dynamics hw ( mostly physics)

MEGR 3121, Dynamics Systems – I

HW # 5, Due: April 2, 2014

Max: 300

Free body diagrams (force diagram and acceleration diagram) are MANDATORY.

Clearly indicate the coordinate systems you are using to solve the problem.

While using F = ma, draw not only force diagram, but also acceleration diagram

Your work should be legible and your own.

1) A bag is gently pushed off the top of a wall at A and swings in a vertical plane at the end

of a rope of length l. Determine the angle θ for which the rope will break, knowing that it can

withstand a maximum tension equal to twice the weight of the bag.

2) Beginning from rest when θ=15°, a 35-kg child slides with negligible friction down the

sliding board which is in the shape of a 2.5-m circular arc. Determine the tangential

acceleration and speed of the child, and the normal force exerted on her (a) when θ=30°

(b) θ=90°

3) Determine the tension in the cables and accelerations of block A and B. Take g = 10

m/s 2

4) A small object A is held against the vertical side of the rotating cylindrical container of

radius r. If the coefficient of static friction between the object and the container is μs,

determine the minimum angular velocity ω of the container which will keep the object

from slipping down the vertical side.

5) The member OA rotates about the horizontal axis through O with a constant

counterclockwise angular velocity ω = 3 rad/sec. As it passes the position θ = 0, a small

block of mass 0.1 kg is placed on it at a radial distance r = 18 inches. If the block is

observed to slip at θ = 50°, determine the coefficient of static friction μs between the

block and the member.

6) Calculate the acceleration of the 100-lb cylinder for each of the two cases illustrated.

Neglect friction and mass of pulleys. Note lb here is unit of force. (Take g = 32.2 ft/s 2 )

7) Find the minimum value of T (i.e. Tmin) for which the block shown in the figure will

start to slip. Next, assume T = 2Tmin and compute the acceleration of the block.

8) A stretch of highway includes a succession of evenly spaced dips and humps, the

contour of which is approximately given by (

) [quite probable in San

Francisco]. What is the maximum speed at which the car A can go over a hump and still

maintain contact with the road? If the car maintains this critical speed, what is the normal

force that it experiences from the ground at the bottom of a dip? The mass of the car is m.

9) The small cart is nudged with negligible initial speed from its horizontal position at A

onto the parabolic path, which lies in a vertical plane. Neglect friction.

a) Find the expression of the normal force N as a function x

b) Show that N is always > 0 for all values of k. [This would essentially mean the cart

stays in contact with the track for all time].

Also, note y is positive down.

10) For the pulley system shown, find the acceleration of the load m and the tension in

the cables. Assume frictionless surfaces, massless pulleys and inextensible cables. The

pulleys C and D are at the same level. Further assume the m/4 blocks and the pulleys C

and D are placed symmetrically about the dotted center line.

m/4 m/4

C D