System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 3, Problem 3.4P
A particle of mass
Start Figure P3.4 
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Block A (m = 5 kg), seen in the figure, sits on a smooth surface and is attached by a slender rod to a ball-and-socket joint at B. If the moment and force shown are simultaneously applied to the block, what will the speed of the block be after 4 seconds (starting from rest)?
Q2
A sack in Figure Q2 with a mass of 2.5kg slides down a smooth surface of a curve
described y =
0.05e0.5x
*. At point A, the sack has a speed of 1.8 m/s.
(a)
Sketch the inertial coordinate and FBD to indicate all the external forces acting
on the sack.
(b)
Using equation of motion, solve the normal reaction that the ramp exerts on
the sack at point A.
y= 0.05e0.5x
1.65 m
Figure Q2
A 25.5 kg mass (m) is suspended by the cable assembly as
shown in the figure. The cables have no mass of their own.
The cable to the left (T) ) of the mass makes an angle of
0.00 with the horizontal, and the cable to the right (T;)
makes an angle (02) of 40.6. If the mass is at rest, what is
the tension in each of the cables, T and T; ? The
acceleration due to gravity is g = 9.81 m/s?.
T
T =
123.52
N
123.52
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Chapter 3 Solutions
System Dynamics
Ch. 3 - Prob. 3.1PCh. 3 - A baseball is thrown horizontally from the...Ch. 3 - For the mass shown in Figure 3.1.3b. m=10 kg, =25...Ch. 3 - A particle of mass m=19 kg slides down a...Ch. 3 - A particle of mass m slides down a frictionless...Ch. 3 - A radar tracks the flight of a projectile (see...Ch. 3 - Table 3.2.1 gives the inertia IO for a point mass...Ch. 3 - A motor supplies a moment M to the pulley of...Ch. 3 - Figure P3.9 shows an inverted pendulum. Obtain the...Ch. 3 - The two masses shown in Figure P3.10 are released...
Ch. 3 - The motor in Figure P3.11 lifts the mass mL by...Ch. 3 - Instead of using the system shown in Figure 3.2.6a...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the cart shown in Figure P3.13. Suppose...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Consider the spur gears shown in Figure P3.15,...Ch. 3 - Derive the expression for the equivalent inertia...Ch. 3 - Prob. 3.18PCh. 3 - The geared system shown in Figure P3.19 represents...Ch. 3 - Prob. 3.20PCh. 3 - Prob. 3.21PCh. 3 - Prob. 3.22PCh. 3 - For the geared system shown in Figure P3.23,...Ch. 3 - For the geared system discussed in Problem 3.23,...Ch. 3 - The geared system shown in Figure P3.25 is similar...Ch. 3 - Consider the rack-and-pinion gear shown in Figure...Ch. 3 - The lead screw (also called a power screw or a...Ch. 3 - Prob. 3.29PCh. 3 - Derive the equation of motion of the block of mass...Ch. 3 - Assume the cylinder in Figure P3.31 rolls without...Ch. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A slender rod 1.4 m long and of mass 20 kg is...Ch. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - The pendulum shown in Figure P3.38 consists of a...Ch. 3 - Prob. 3.39PCh. 3 - A single link of a robot arm is shown in Figure...Ch. 3 - 3.41 It is required to determine the maximum...Ch. 3 - Figure P3.42 illustrates a pendulum with a base...Ch. 3 - Figure P3.43 illustrates a pendulum with a base...Ch. 3 - 3.44 The overhead trolley shown in Figure P3.44 is...Ch. 3 - Prob. 3.45PCh. 3 - The “sky crane” shown on the text cover was a...
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- (b) An aircraft, of mass 2000 kg, is following a circular path in the vertical plane as shown in Figure 2. When the flight path of the aircraft is at an angle of 30° from the horizontal, the aircraft's velocity is 150 m/sec, the radius of curvature of its trajectory is 1000 metres, and the net thrust (engine thrust minus drag) is T = 30 kN and acts along the flight path. Assume that the lift force L is perpendicular to the flight path. Draw a free-body diagram showing all forces acting on the aircraft. Calculate the resultant acceleration and its angle from the flight path. Also calculate the lift force L. = 1000 metres 30 Figure 2arrow_forwardQuestion 1: A sphere of mass m = 2 kg, is released from rest at point A (see Figure 1.1). Due to gravity, the sphere goes down the path AB (which is an inclined plane, at 45 degrees from the horizontal line) and then hits the ground at point D; the vertical wall BC is 2000 cm high (see Figure 1.1 for details) Assume no friction. (a) Derive the velocity of the sphere when it reaches point B. (b) Derive the distance CD and the time the sphere takes to go from point B to point D. State and justify your assumptions and comment on your working. Marks will be assigned for the quality of the presentation of the working and of the comments. (You have to assign the value of L, in centimetres, by using the last 3 digits of your student ID, and then solve the question; for example, if your student ID is 19980169, then L=169 cm; if your ID is 17680039, then L=39 cm; if your ID is 14567000, then L=1000 cm). L L C B D L = 50 cm in this Figure 1.1 case...arrow_forwardIn a modified version of the cart and bucket, the angle of the slope is alpha = 34.9∘ and the bucket weighs 295 N. The cart moves up the incline and the bucket moves downward, both at constant speed. The cable has negligible mass, and there is no friction. What is the weight of the cart?What is the tension in the cable?arrow_forward
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