A dumbbell is composed of two particles, each of mass m, connected by a massless rod of length l. One particle of the dumbbell is connected by a pivot to the edge of a disk of radius r, which is massless except for a particle of mass m at its center. The disk can roll without slipping on a horizontal surface, and all motion occurs in the vertical plane of the disk. Assuming that θ and Ø are the absolute rotation angles of the disk and dumbbell, as shown, obtain the differential equations of motion. Use Lagrange Eqn.

A dumbbell is composed of two particles, each of mass m, connected by a massless rod of length l. One particle of the dumbbell is connected by a pivot to the edge of a disk of radius r, which is massless except for a particle of mass m at its center. The disk can roll without slipping on a horizontal surface, and all motion occurs in the vertical plane of the disk. Assuming that θ and Ø are the absolute rotation angles of the disk and dumbbell, as shown, obtain the differential equations of motion. Use Lagrange Eqn.

Related questions

Q: At the instant of the figure, a 1.3 kg particle P has a position vector 7 of magnitude 1.4 m and…

A: Angular momentum, L = m(r × v) L = mrv sin (180 - θ2) k L = mrv sin(180 - 30) k L =…

Q: A small, spherical asteroid of mass 6500000 kg and radius 7.6 m is stationary. The unsuspecting…

A: Given, Mass of asteroid , M = 6500000 kgRadius, R = 7.6 mMass of car, m = 1320 kgSpeed of Tesla car,…

Q: In a laboratory experiment, a very large fish tank is filled with water. At the bottom of the tank,…

A: a) It is given that for the laboratory experiment, a large fish tank is taken and a rigid rod of…

Q: In the figure, two blocks, of mass m₁ = 478 g and m₂ = 740 g, are connected by a massless cord that…

Q: A thin circular ring of mass m and radius R is rotating about its axis with a constant angular…

A: mω/(m+2M)

Q: A block of mass m1 = 30.0 kg (starting from the rest) is going down an inclined plane at angle θ =…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: You are looking down on a disc that is spinning counterclockwise in the xy plane (positive z points…

Q: A puck of mass m = 1.10 kg slides in a circle of radius r = 17.0 cm on a frictionless table while…

Q: 上。 M 20 ②

A: Given that: The mass of the block is M The mass of the bullet is m The velocity of the bullet is vb…

Q: A uniform rod of mass 230 g and length 100 cm is free to rotate in a horizontal plane around a fixed…

Q: In the figure below, two blocks, of mass m, = 380 g and m2 = 800 g, are connected by a massless cord…

A: Given that, m1=0.380 kgm2=0.800 kgM=0.500 kgR=0.12 m The free body diagram of the two blocks are…

Q: The figure above shows a small sphere of mass m at a height H from the center of a uniform ring of…

A: The x-component of the gravitational force Fx is given by the projection of the gravitational force…

Q: The figure below shows four spheres at the corners of a rectangle, connected by rods of negligible…

A: Given that The masses of the four sphere are m1 =2.50kg m2=1.50kg m3=3.70kg m4=1.70kg The width of…

Q: A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.863 rad/s.…

A: Given Data: Angular velocity of the platform (ωp) = 0.863 rad/s.Mass of the person (mp) = 69.1…

Q: Problem 5: A bus contains a 1560 kg flywheel (a disk that has a 0.55 m radius) and has a total mass…

A: (a) The translational K.E. of the bus at the speed, 15 m.s-1 be calculated as,

Q: Two disks each have a mass of 5 kg and a radius 300 mm. They spin as shown at the rate of w1 = 1200…

A: Given: Two disks each have a mass of 5 kg and a radius 300 mm. They spin as shown at the rate of w1…

Q: In a rotational equilibrium experiment, a group takes a one-meter ruler with a uniformly distributed…

A: Given,mass of the ruler M =250gm1=170g at 20cmm2=155g at 40cmm3 is placed at 15cm

Q: A space of mass 120 kg is going to use a planet for a gravitational assist- that is, use the…

Q: In the figure, two blocks, of mass m1 = 341 g and m2 = 526 g, are connected by a massless cord that…

Q: A marble with mass m = 9 g at the end of a massless string is swaying in a circle of radius R = 1.65…

Q: small, spherical asteroid of mass 6500000 kg and radius 7.6 m is stationary. The unsuspecting space…

A: Given, Mass of asteroid , M = 6500000 kgRadius, R = 7.6 mMass of car, m = 1320 kgSpeed of Tesla car,…

Q: A physical pendulum consists of a vertical board of of mass 6.52 kg. length 195 cm, and width 13 cm…

A: The mass of the board: M=6.52 kg The length of the board: L=195 cm=1.95 m The width of the board:…

Q: You are in a carnival ride that consists of a circular room that spins around its center. You stand…

Q: A boy of mass m runs with speed v tangentially toward a merry-go-round of mass M and radius R, which…

A: Given: The mass of the man is m. The speed of the man is v. The mass and radius of the…

Q: y can slide along the rod. They are initially held by clips at positions 0.05 cm on each side of the…

A: Given: mass of rod, M = 0.03 kg length of rod, l = 0.2 m mass of each body, m = 0.02 kg distance…

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Explanation,

VIEW

Step 2: The potential energy of the dumbbell is given by,

VIEW

Step 3: We use lagrangian mechanics

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A skateboard of mass m rests on the top of a hemispheric dome of radius R. After giving the skateboard a small kick, imparting an initial speed of vo, it begins rolling down the dome. Let the angle 0 indicate the location of the skateboard as it rolls down the surface of the dome. R 1. Eventually, the skateboard will lose contact with the dome. Given m, R, vo, and g, find the angle 0. at which the skateboard loses contact. Express your answer symbolically (i.e. without numbers). Check your work. Suppose you choose m = 1.5 kg, vo = g = 9.81 m/s. In this case, your answer should evaluate to 0. = 34.2°. 4.5 m/s, R = 4.3 m, and 2. Given m, R, and g, determine the range of speeds for which it is impossible to remain in contact with the wall at all.
A physical pendulum consists of a vertical board of of mass 5.8 kg, length 172 cm, and width 5 cm hanging from a horizontal, frictionless axle. A bullet of mass 145 g and a purely horizontal speed v impacts the pendulum at the bottom edge of the board. The board then makes a complete circle. (a) If the bullet embedded itself in the board, what is the minimum speed the bullet could have to make this so? (b) If the bullet passed through the board, reducing its speed by 1/5 its original value, what is the minimum speed of the bullet? (c) If the bullet is made of rubber and rebounds elastically, what is the minimum speed the bullet could have? (d) What is the rebound speed of the bullet?
In the figure, two blocks, of mass m1 = 257 g and m2 = 337 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 492 g and radius R = 10.1 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T1 in the cord at the left and (c) the tension T2 in the cord at the right. M R T2 (a) Number i 0.095238 Units m/s^2 (b) Number Units (c) Number i Units
A child's top is held in place upright on a frictionless surface. The axle has a radius of r 3.21 mm. Two strings are wrapped around the axle, and the top is set spinning by T T applying T = 2.40 N of constant tension to each string. If it takes 0.590 s for the string to unwind, how much angular 2r momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. R SP 9.15 x10¬3 kg-m² L = S Point P is located on the outer surface of the top, a distance h = 35.0 mm above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is 0 = 24.0°. If the final tangential speed v, of point P is 1.45 m/s, what is the top's moment of inertia I? T 2r T 2.42 x10-4 kg-m? = Incorrect
0.1/1E: In the figure, two blocks, of mass m1 = 257 g and m2 = 337 g, are connected by a massless cord that-is wrapped around a uniform disk of mass M = 492 g and radius R = 10.1 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T in the cord at the left and (c) the tension T2 in the cord at the right. %3D %3! R. (a) Number i Units m/s^2 (b) Number i Units (c) Number Units eTextbook and Media 898 MAY 1 PDF 8 tv .. DD 80 000 000 888 F9 F10 F11 F6 F7 FB F2 F3 F4 F5 @ 23 2$ & 2 3 4 7 8 9
In a rotational equilibrium experiment, a group takes a one-meter ruler with a uniformly distributed mass of 250 grams. A thread will be tied to the ruler 15 cm to the left of the center of mass, swinging the ruler. Then the group places a mass m1 = 170 gr at the 20 cm position on the ruler. Then they place a mass m2 = 155 gr in the 40 cm position. What must be the value of a mass m3 placed at the 15 cm position on the ruler for the system to remain in equilibrium?
Consider a disc of mass 0.44kg, with radius 0.5 m on a slope with angle 45 degrees to the horizontal. It has a good grip on the slope and does not slip. The disc is constructed so that its mass per unit area, ρ(r) = r1/2 kg m−2, with r being the radial distance in metres from the axis of the disc. What is the acceleration of the disc down the slope?
A 4-Kilogram object slides, on a smooth surface, towards the north at a velocity of 5 meters per second. The object hits a fixed pole and is deflected from north to east by an angle of 60° and has a velocity of 5 meters per second. The change in the magnitude of the northward component of the moment of the object is
In the figure, two blocks, of mass m₁ = 289 g and m₂ = 362 g, are connected by a massless cord that is wrapped around a uniform disk of mass M = 533 g and radius R = 11.3 cm. The disk can rotate without friction about a fixed horizontal axis through its center; the cord cannot slip on the disk. The system is released from rest. Find (a) the magnitude of the acceleration of the blocks, (b) the tension T₁ in the cord at the left and (c) the tension T₂ in the cord at the right. M (a) Number i (b) Number (c) Number i Units Units Units 081 R Ng
A disk of radius R and mass M has initial angular velocity ωi. It is flat on a horizontal surface and friction is present. The center of mass speed is zero (always) in this problem. Find the time it takes for the disk to stop spinning.