ES8: DYNAMICS IN RIGID BODIES MAY 21, 2025

WORKSHEET #5
BSME – 2A
PROBLEMS
1127. Solve Illus. Prob. 1126 using the following data: W = 100 lb; 𝑣 = 8.03 ft per sec; L = 18 in.

1128. A rod 4 ft long rotates in a horizontal plane about a vertical axis through its center. At each of the rod is fastened
a cord 3 ft long. Each cord supports a weight W. Compute the speed of rotation n in rpm to incline each cord at 30° with
the vertical.
1129. A weight concentrated at the end of a cord forms a conical pendulum for which the period is 1 sec. Determine the
velocity v of the weight if the cord rotates inclined at 30° with the vertical.

1130. In Fig. P-1130, the 20-lb ball is forced to rotate around the smooth inside surface of a conical shell at the rate of
𝜋
the revolution in sec. Assuming that g = 32.0 ft per sec2, find the tension in the cord and the force on the conical shell.
4
At what speed in rpm will the force on the shell become zero?
1131. A body of weight W rests on the smooth inclined surface of the frame shown in Fig. P-1131. A peg attached to
the frame forces the body to rotate with it about the vertical axis. Determine the speed in rpm at which the tension in the
cord is equal to the weight of the body.

1132. The hammer of an impact testing machine weighs 64.4 lb. As shown in Fig. P-1132, it is attached to the end of 𝑢
light rod 4 ft long which is pivoted to a horizontal axis at A. (a) What is the bearing reaction on the pivot an instant after
being released from the given position? (b) What is the bearing reaction just before impact at B is the velocity of the
hammer is then 5.9 ft per sec?
1133. To check the radius of a railroad curve, the effect of a 20-lb weight is observed to be 20.7 lb on a spring scale
suspended from the roof of an experimental car rounding the curve at 40 mph. What is the radius of the curve?

1134. Figure P-1134 represents a schematic diagram of a Porter governor. Each flyball weighs 16.1 lb and the central
weight D is 40 lb. Determine the rotational speed in rpm about the vertical axis AD at which the weigh D begins to rise.
1135. What counterweight W will maintain the Corliss engine governor in the position shown in Fig. P-1135 at a
rotational speed 𝑛 = 120 rpm. Each flyball weighs 16.1 lb. Neglect the weight of the other links.

1136. The side rod of the engine in Fig. P-1136 is 8 ft long and weighs 100 lb. The cranks AD and BC are if length r =
𝑊𝐿
18 in and rotates at 300 rpm. Determine the maximum bending moment M in the rod if M = , where W is the total
8
distributed load and L is the length of the rod.
 4𝑥 𝑥2
1137. The segment of road passing over the crest of a hill is defined by the parabolic curve 𝑦 = − . A car weighing
10 100
3220 lb travels along the road at a constant speed of 30 ft per sec. What is the pressure on the wheels of the car when it
is at the crest of the hill where y = 4ft? At what speed will the road pressure be zero?
ⅆ2 𝑦
1 ⅆ𝑥2
Hint: The radius of the curvature is defined by = 3 .
𝜌
ⅆ𝑦 2 2
[1+(ⅆ𝑥) ]

1138. A homogeneous triangular plate weighing 64.4 lb is attached to a rigid vertical support by two weightless links
as shown in Fig. P-1138. At the position shown, the plate has an upward velocity of 12 ft per sec. Compute the total
force acting on pin C.
1140. Why are railroad curves laid out in the form of a spiral with a gradually decreasing radius of curvature instead of
a circle of constant radius?

1141. A boy running a foot race rounds a flat curve of 50-ft radius. If he runs at the rate of 15 mph, at what angle with
the vertical will be incline his body?
1142. A daredevil drives a motorcycle around a circular vertical wall 100 ft in diameter. The coefficient of friction
between tires and wall is 0.60. What is the minimum speed that will prevent his sliding down the wall? At what angle
will the motorcycle be inclined to the horizontal? What is the effect of traveling at a greater speed?

1143. The superelevation of a railroad track is the number of inches that the outside rail is raised to prevent side thrust
on the wheel flanges of cars rounding the curve at rated speed. Determine the superelevation 𝑒 for a track having a gauge
1
of 4 ft 8 in of 2000-ft radius and a rated speed of 60 mph. What is the flange pressure P on the wheels of a 100,000-lb
2
car that rounds the curve at 80 mph?
1144. An airplane makes a turn in a horizontal plane without sideslip at 480 mph. At what angle must the plane be
banked if the radius of the turn is 1 mile? If the pilot weighs 150 lb, what pressure does he exert on his seat?

1145. A car weighing 3220 lb rounds a curve of 200-ft radius banked at an angle of 30°. Find the friction force acting
on the tired when the car is traveling at 60 mph. The coefficient of friction between the tires and the road is 0.90.
1146. Find the angle of banking for a highway curve of 300-ft radius designed to accommodate cars traveling at 100
mph, if the coefficient of friction between the tires and the road is 0.60. What is the rated speed of the curve?

1147. The rated speed of a highway curve of 200-ft radius is 30 mph. If the coefficient of friction between the tires and
the road is 0.60, what is the maximum speed at which a car can round the curve without skidding?
1148. The coefficient of friction between the road and the tires of the car shown in Fig. P-1148 is 0.60. The car weighs
3220 lb. It is rounding the curve of 500-ft radius at maximum speed. What is the value of the friction force acting under
each wheel? How high above the road must the center of gravity be to limit this maximum speed by the tendency to
overturn?

1149. Repeat Prob. 1148 if the road is banked at 20° instead of 30° as shown in Fig. P-1148.
1220. A weight of 96.6 lb is fastened to a cord which is wrapped around a solid cylinder of 3 radius weighing 322 lb.
The cylinder rotates about its horizontal centroidal axis. Compute the angular accelerations and the tension in the cord;
also the total bearing reaction.

1221. What torque applied to the cylinder of Prob. 1220 will raise the weight with an acceleration of 12 ft peer sec2?
What will be the total bearing reaction?
1222. During the operation of a punch press, its flywheel decelerates uniformly from 400 rpm to 200 rpm in 1 sec. The
rim of the flywheel weighs 1288 lb, its inside and outside diameters are 56 in and 60 in, and it is attached to its hub by
6 spokes. What average shearing force is developed between the rim and each spoke during the 1 sec interval?

1223. The compound pulley in Fig. P-1223 has a centroidal mass moment if inertia of 20 ft-lb-sec2. Find the tension in
the cord supporting the 161-lb weight.
1224. Determine the time required for the compound pulley shown in Fig. P-1224 to reach a speed of 600 rpm starting
from rest.

1225. To what value should the weight of A in Fig. P-1224 be changed to give it a downward acceleration of 9 ft per
sec2?
1226. If the weight shown in Fig. P-1226 is descending freely, determine the tension in the cord both before and after a
brake force P = 100 lb is applied. Neglect thickness of brake.

1227. If the drum in Fig. P-1226 is rotating clockwise at 120 rpm, solve for the brake force P required to bring the
system to rest in 5 sec. Assume the brake block to be 6 in thick. The coefficient of kinetic friction at the brake is 0.20.
1228. Find the tension in the cord attached to the block A in Fig. P-1228. Neglect the weight of the floating pulley
supporting weight B.

1229. Compute the tension in the cord attached to block A in Fig. P-1229. The coefficient of kinetic friction under both
blocks is 0.20.
1230. Determine the maximum weight of A that will permit the 400-lb block B to slide without tipping over.

1231. In the system in Fig. P-1231, block A has a downward velocity of 48 ft per sec at the instant the brake is applied.
What is the tension in the cord between A and B after the brake is applied? How far will block A have moved 2 sec after
the brake is applied? Neglect thickness of brake.
1232. Assume the maximum strength of the cord supporting block A in Fig. P.1231 is 700 lb and of that joining drums
B and C is 1200 lb. If the brake is applied too suddenly, one of these cords will fail. Which one will it be and at what
brake from P?

1235. A 3220-lb flywheel is fastened to the midpoint of a shaft 6 ft long. The center of gravity of the flywheel is 0.01
in from the axis of rotation. The flywheel rotates at a constant speed of 1800 rpm. Determine the maximum and minimum
values of the bearing reactions at each end of the shaft.
1236. A uniform slender rod 6 ft long that weighs 64.4 lb is suspended vertically at one end. A horizontal force of 32 lb
is applied at the midpoint of the rod. Determine the horizontal reaction of the axis on the rod. Where should the force
be applied to make the horizontal reaction zero? (This point is called the center of percussion).

1237. The uniform slender rod in Fig. P-1237 weighs 96.6 lb and is supported on knife edges at A and B. Determine the
reaction at A the instant after the support at B is suddenly removed.
1238. Aman weighing 161 lb is seated on a horizontal turntable 2 ft away from the vertical axis of rotation, as shown in
Fig. P-1238. The coefficient of friction between him and the turntable is 0.40. If the turntable starts from rest and
1
accelerates at the rate of rad per sec2, how many seconds will elapse before he starts to slide? Determine the angle 𝜃
2
of the direction in which he will slide.

1239. A uniform slender rod is hinged to a frame rotating about a vertical axis as in Fig. P-1239. Show that the angle
3𝑔
between the rod and the axis is defined by 𝑐𝑜𝑠 𝜃 = 2 .
2𝐿𝜔
1940. A uniform slender rod weighing 96.6 lb is fastened to the rotating frame in Fig. P-1240 by a smooth hinge at A
and a horizontal cord at B. The frame rotates about its vertical axis at a constant speed of 4 rad per sec. Find the tension
in the cord and the horizontal and the horizontal and vertical components of the hinge reaction.

1241. Determine the speed of rotation in rpm at which the cord in Prob.1240 will have a tensile force of 200 lb.
1242. A uniform slender rod b ft long and weighing 𝛾 lb per ft is fastened at its midpoint to a horizontal shaft as shown
in Fig. P-1242. The rod is attached to the shaft midway between two bearings A and B a distance L ft a part. Compute
the dynamic reactions at A and B when the shaft is rotating at 𝜔 rad per sec.

1243. Two blocks having the weights and positions shown in Fig. P-1243 rest upon a frame which rotates about its
vertical axis at a constant speed. The coefficient of friction between the blocks and the frame is 0.20. The weight and
friction of the pulley being neglected, at what speed in rpm will the blocks start to slide? What is the tension in the cord
at this instant?
1244. Repeat Prob. 1243 if the weights of the blocks are interchanged.

1245. Three bars, each 2 ft long and weighing 9.66 lb, are pinned together to form the equilateral frame shown in Fig.
P-1245. They rotate in a horizontal plane about a vertical axis at A. What torque is required to cause an angular
acceleration of 12 rad per sec2? What is the reaction at A when the frame reaches a speed if 38.2 rpm?
1246. The bent bar shown in Fig. P-1246 weighs 16.1 lb per ft. It rests on a smooth horizontal surface and rotates about
a vertical axis through A. Compute the torque required to cause a counterclockwise acceleration of 6 rad per sec2. What
are the X and Y components of the reaction at A when the speed is 3 rad per sec?

1247. The bent bar shown in Fig. P-1246 weighs 16.1 lb per ft and is free to rotate in a vertical plane about a horizontal
axis at A. Compute X and Y components of the bearing reaction at A an instant after it is released from rest at the given
position.
1248. The system shown in Fig. P-1248 consist of a circular disk welded to the end of a uniform bar. The assembly
rotates in a vertical plane about a horizontal axis at A. At the given position, the angular velocity is 4 rad per sec.
Compute the magnitude of the bearing reaction.

1249. At the instant shown in Fig. P-1249, the body B has a clockwise angular velocity of 5 rad per sec. The horizontal
cord joining A and B passes over a weightless and frictionless pulley. Determine the horizontal and vertical components
of the axle reaction at Z.
1250. The rotating assembly shown in Fig. P-1250 consists of an unbalanced pulley to which is bolted a uniform rod
carrying a sphere at its end. The pulley rotates about a horizontal axis at Z and has a 1 ft radius of gyration about its
gravity center G. Show that the mass moment of inertia about Z is 𝐼𝑧 = 45.5 ft-lb-sec2 and then compute the angular
acceleration of the pulley and the tension of the cord.

1251. At the instant shown in Fig. P-1250, the system has a clockwise angular velocity of 4 rad per sec. Using the results
of Prob. 1250, compute the horizontal and vertical components of the bearing reaction at Z.
1252. Two eccentric weights, W1 = 100 lb and W2 = 200 lb, are fastened to he rotating horizontal shaft AB shown Fig.
P-1252. Compute the values of balance weights concentrated 1 ft from the shaft and rotating in vertical planes through
A and B that will balance the dynamic effects of W1 and W2. What are the angular positions of the balance weights
measured from the plane containing W1 and axis AB?