Two uniform solid spheres are joined by a light rigid rod to form a dumbbell. The...

Two uniform solid spheres are joined by a light rigid rod to form a dumbbell. The spheres are identical, and each has mass M/2. One end of a spring is attached to the center of the rod, the spring is stretched perpendicular to the rod, and the other end of the spring is attached to a wall. The dumbbell rests on a horizontal surface. Friction between the surface and the spheres prevents slipping. The system is released from rest.

a) Show that as the dumbbell rolls, its center of mass executes simple harmonic motion.

b) Find the period of the oscillations.

Solutions

Expert Solution

Solution in the uploaded image

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Two identical uniform solid spheres are attached by a solid uniform thin rod, as shown in the figure.

Two identical uniform solid spheres are attached by a solid uniform thin rod, as shown in the figure. The rod lies on a line connecting the centers of mass of the two spheres. The axes A, B, C, and D are in the plane of the page (which also contains the centers of mass of the spheres and the rod), while axes E and F (represented by black dots) are perpendicular to the page. (Figure 1).Rank the moments of inertia...

A pendulum consists of a light rigid rod of length 250 mm, with two identical uniform...

A pendulum consists of a light rigid rod of length 250 mm, with two identical uniform solid spheres of radius 50 mm attached one on either side of its lower end. Find the period of small oscillations (a) perpendicular to the line of centers and (b) along it.

Two identical, uniform and frictionless spheres, each of mass m, rest in a rigid rectangular container...

Two identical, uniform and frictionless spheres, each of mass m, rest in a rigid rectangular container as shown in the figure. A line connecting their centers is at 45° to the horizontal. a)If the angle is increased to 90° think about what happens to the forces. This can help provide a check to your answers as we make a change to the problem. For all of the following questions, the configuration is now changed such that the line connecting their...

A light, rigid rod of length ℓ = 1.00 m joins two particles, with masses...

(a) A light, rigid rod of length ℓ = 1.00 m joins two particles, with masses m = 4.00 kg and m, = 3.00 kg, at its ends. The combination rotates in the xy-plane about a pivot through the center of the rod (see figure below). Determine the angular momentum of the system about the origin when the speed of each particle is 7.60 m/s. (Enter the magnitude to at least two decimal places in kg. m2/s.) (b) What If? What would...

A pendulum is constructed from a thin, rigid, and uniform rod with a small sphere attached...

A pendulum is constructed from a thin, rigid, and uniform rod with a small sphere attached to the end opposite the pivot. This arrangement is a good approximation to a simple pendulum (period = 5.87 s), because the mass of the sphere (lead) is much greater than the mass of the rod (aluminum). When the sphere is removed, the pendulum is no longer a simple pendulum, but is then a physical pendulum. What is the period of the physical pendulum?

(a) A light, rigid rod of length 1.00 m joins two particles, with masses m-4.00 kg...

(a) A light, rigid rod of length 1.00 m joins two particles, with masses m1 = 4.00 kg and m2 = 3.00 kg, at its ends. The combination rotates in the xy-plane about a pivot through the center of the rod (see figure below . Determine the angular momentum of the system about the origin when the speed of each particle is 4.40 m/s. (Enter the magnitude to at least two decimal places in kg·m2/s. (b) What I? What would be...

Two uniform solid spheres, each with mass 0.800 kg and radius 8.00×10−2 m, are connected by...

Two uniform solid spheres, each with mass 0.800 kg and radius 8.00×10−2 m, are connected by a short, light rod that is along a diameter of each sphere and are at rest on a horizontal tabletop. A spring with force constant 157 N/m has one end attached to the wall and the other end attached to a frictionless ring that passes over the rod at the center of mass of the spheres, which is midway between the centers of the...

Two identical metal spheres A and B are connected by a plastic rod.

Two identical metal spheres A and B are connected by a plastic rod. Both are initially neutral. 4.0×1012 electrons are added to sphere A, then the connecting rod is removed. a)Afterward, what is the charge of A? b)Afterward, what is the charge of B?

A grinding wheel is in the form of a uniform solid disk of radius 6.96 cm...

A grinding wheel is in the form of a uniform solid disk of radius 6.96 cm and mass 2.05 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.606 N · m that the motor exerts on the wheel. (a) How long does the wheel take to reach its final operating speed of 1 190 rev/min? s (b) Through how many revolutions does it turn while accelerating? rev

Two solid metal spheres of different radii are far apart. The spheres are connected by a fine metal wire. Some charge is placed on one of the spheres.

Two solid metal spheres of different radii are far apart. The spheres are connected by a fine metal wire. Some charge is placed on one of the spheres. After electrostatic equilibrium is reached, the wire is removed. Which of these quantities will be the same for the two spheres?(a) The charge on each sphere(b) The electric field inside each sphere, at the same distance from the center of the spheres(c) The electric field just outside the surface of each sphere(d)...

Subjects