A small body of mass m performs small oscillations sliding (no rolling) along the bottom of...
A small body of mass m performs small oscillations sliding (no rolling) along the bottom of a vertical circle of radius R under the action of the gravitational force. The initial distance from the equilibrium (bottom) point is x0 (along the horizontal axis), the initial velocity is absent. The friction coefficient between the body and the circle is "μ". Assume that the energy loss per period is small. Find the duration of the motion before the body stops.
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A small body of mass m performs small oscillations sliding (no
rolling) along the bottom of...
A block sliding to the right along a horizontal frictional surface has an initial velocity of...
A block sliding to the right along a horizontal frictional surface has an initial velocity of 12.4 m/s and stops in 110 m due to friction with the surface. Find the acceleration of the block. Find the coefficient of kinetic friction between the block and the surface.
7090 2. A circular rigid body of mass m and radius of gyration k is released...
7090 2. A circular rigid body of mass m and radius of gyration k is released from stationary in an incline plane of incline angle θ and coefficient of friction μ Determine the normal reaction force, friction force, linear and angular accelerations when it is in (1) pure rolling motion. (2) rolling with slipping motion. (3) Compare a cylinder (radius of gyration k 1/ 2) and a hoop (k- 1) of the same mass, which one travels faster along the...
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5, Some of the funniest videos on the web involve motorists sliding uncontrollably on icy roads. Here let's compare the typical stopping distances for a car sliding to a stop from an initial...
5, Some of the funniest videos on the web involve motorists sliding uncontrollably on icy roads. Here let's compare the typical stopping distances for a car sliding to a stop from an initial speed of 10.0 m/s on a dry horizontal road, an icy hori- zontal road, and (everyone's favorite) an icy hill. (a) How far does the car take to slide to a stop on a hori- zontal roadi if the coefficient of kinetic friction is = 0.60, which...
1. The small mass m is to slide down the large mass M without friction. The...
1. The small mass m is to slide down the large mass M without friction. The track along which the small block slides is a quarter circle with radius R. The large mass itself is free to move on a frictionless horizontal surface. Initially both masses are at rest with the small mass at the top of the quarter circle, as shown in the figure. (a) (5 Pts.) What is the initial total mechanical energy with respect to the horizontal...
The subject is circular motion, thanks for your help! Hoop 2. A small bead of mass...
The subject is circular motion, thanks for your help!
Hoop 2. A small bead of mass M can slide without friction on a circular hoop that is in a vertical plane and has a radius L. The hoop rotates about a vertical diameter, as shown in the figure. It takes time T to complete one revolution. You observe that the bead is located at an angle with respect to the vertical. It is moving in a horizontal circle (dashed line)...
A small bead of mass m can slide without friction on a circular hoop that is...
A small bead of mass m can slide without friction on a circular hoop that is in a vertical plane and has a radius R. The hoop rotates at a constant angular velocity ω about a vertical axis through the diameter of the hoop. Our goal is to find the angle β, as shown, such that the bead is in vertical equilibrium. We break the problem into several steps. a) Assume the bead is in vertical equilibrium and does not...
A 75-kg volleyball player performs a maximum-effort vertical jump with an initial velocity of 3 m/s....
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A bead of mass m slides frictionlessly on a circle of wire with radius R. The...
A bead of mass m slides frictionlessly on a circle of wire with radius R. The circle stands up in a vertical plane and rotates about the z-axis with constant angular velocity . Write down the Lagrangian. Find the equations of motion. For an angular velocity greater than some critical angular velocity , the bead will experience small oscillations about some stable equilibrium point . Find and (). We were unable to transcribe this imageWe were unable to transcribe this...
A small object of mass m moves in a horizontal circle of radius r on a...
A small object of mass m moves in a horizontal circle of radius r on a rough table. It is attached to a horizontal string fixed at the center of the circle. The speed of the object is initially v0. After completing one full trip around the circle, the speed of the object is 0.5v0. (a) Find the energy dissipated by friction during that one revolution in terms of m, v0, and r. (Use any variable or symbol stated above...
7090 2. A circular rigid body of mass m and radius of gyration k is released from stationary in an incline plane of incline angle θ and coefficient of friction μ Determine the normal reaction force, friction force, linear and angular accelerations when it is in (1) pure rolling motion. (2) rolling with slipping motion. (3) Compare a cylinder (radius of gyration k 1/ 2) and a hoop (k- 1) of the same mass, which one travels faster along the...
A bead of mass M is able to move without friction along a stationary horizontal rod (directed along the x axis). In addition, a second body of mass m is attached to the first bead and suspended below it via a massless rod of length a. This second mass and rod form a pendulum that is able to swing in the xy-plane (where y is the vertical axis). (a) Obtain the Lagrangian for the system of two masses. (b) Assuming...
5, Some of the funniest videos on the web involve motorists sliding uncontrollably on icy roads. Here let's compare the typical stopping distances for a car sliding to a stop from an initial speed of 10.0 m/s on a dry horizontal road, an icy hori- zontal road, and (everyone's favorite) an icy hill. (a) How far does the car take to slide to a stop on a hori- zontal roadi if the coefficient of kinetic friction is = 0.60, which...
1. The small mass m is to slide down the large mass M without friction. The track along which the small block slides is a quarter circle with radius R. The large mass itself is free to move on a frictionless horizontal surface. Initially both masses are at rest with the small mass at the top of the quarter circle, as shown in the figure. (a) (5 Pts.) What is the initial total mechanical energy with respect to the horizontal...
The subject is circular motion, thanks for your help!
Hoop 2. A small bead of mass M can slide without friction on a circular hoop that is in a vertical plane and has a radius L. The hoop rotates about a vertical diameter, as shown in the figure. It takes time T to complete one revolution. You observe that the bead is located at an angle with respect to the vertical. It is moving in a horizontal circle (dashed line)...
A 75-kg volleyball player performs a maximum-effort vertical jump with an initial velocity of 3 m/s. The player leaves the ground with an upright body position and also touches down with the same body position. Answer the following: ua A. How much will the player's center of mass (COM) travel in the air along the vertical direction during the ascending phase of the jump? Compute the maximum kinetic energy of the player during the jump. C. Compute the maximum potential...
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