10.71
A low-friction cart of mass m rests on a horizontal table. The cart is attached to a relaxed light spring constant k. At distance d from the first cart rests a second identical cart. Both cars are covered with Velcro so they stick together if they collide or touch. The first cart is pushed to the left with initial speed v0.
a) Determine the final frequency of a vibrating system. Consider the case when the right care does not reach the left cart. Express your answer in terms of some or all of the variables k, m, v0, and pi.
When the right cart does not reach the left cart, it is a single
mass spring system
The angular frequency of such system is, w = sqrt(k/m)
frequency, f = w/2pi
f = (1/2pi)*sqrt(k/m) = (1/2pi) √(k/m)
10.71 A low-friction cart of mass m rests on a horizontal table. The cart is attached...
A cart of mass m rolls without friction on a level surface, and is attached to a light spring of constant k, the other end of which is attached to a wall. Take the initial position of the cart, where the spring is neither extended nor compressed, to be the origin x = 0 of a coordinate system where positive x values are to the right and positive vectors point to the right. The cart is pushed to the left...
A cart of mass m rolls without friction on a level surface, and is attached to a light spring of constant k, the other end of which is attached to a wall. Take the initial position of the cart, where the spring is neither extended nor compressed, to be the origin x = 0 of a coordinate system where positive x values are to the right and positive vectors point to the right. The cart is pushed to the left...
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6. Consider a horizontal spring with spring constant k. A block with mass m is pushed far to the left against the spring until the spring is compressed a distance r relative to its relaxed length. A second block, which is stationary and also has a mass m, is located to the right of the spring im rrm a) We release the first block from rest. Due to the force from the spring, it slides to the right and eventually...
A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k. The other end of the spring is attached to a wall (Fig. P14.68). A second block with mass m rests on top of the first block. The coefficient of static friction between the blocks is ms. Find the maximum amplitude of oscillation such that the top block will not slip on the bottom block. Suppose the two blocks are...
6. Consider a horizontal spring with spring constant k. A block with mass m is pushed far to the left against the spring until the spring is compressed a distance r relative to its relaxed length. A second block, which is stationary and also has a mass m, is located to the right of the spring im rrm a) We release the first block from rest. Due to the force from the spring, it slides to the right and eventually...
A block with mass M rests on a frictionless surface and is connected to a horizontal spring of force constant k. The other end of the spring is attached to a wall. A second block with mass m rests on top of the first block. The coefficient of static friction between the a blocks is μs. a) Find the maximum amplitude of oscillation such that the top block will not slip on the bottom block. b) Suppose the coefficient of...
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