# Simple harmonic motion frictionless block problem

• triplel777
In summary, the block must be thrown with a speed greater than 1.85 m/s in order to knock over the bottle, given that it has an angular frequency of 6.6 rad/s and the spring is stretched by 0.056 m. The equation for finding the energy of the system at maximum stretch is 1/2mv_0^2=1/2kd^2, and the energy of the system when the block is launched can be found using the relationship between angular frequency, spring constant, and mass. By assuming energy conservation, the two expressions can be related to find the minimum speed needed to knock over the bottle.
triplel777

## Homework Statement

A block rests on a frictionless horizontal surface and is attached to a spring. When set into simple harmonic motion, the block oscillates back and forth with an angular frequency of 6.6 rad/s. The drawing indicates the position of the block when the spring is unstrained. This position is labeled "x = 0 m." The drawing also shows a small bottle located 0.084 m to the right of this position. The block is pulled to the right, stretching the spring by 0.056 m, and is then thrown to the left. In order for the block to knock over the bottle, it must be thrown with a speed exceeding v0. Ignoring the width of the block, find v0.

## The Attempt at a Solution

1/2mv_0^2=1/2kd^2
d=0.84-0.56=0.28
V_0=sqrt (k/m)*d
V_0= 6.6*0.28= 1.85

what am i doing wrong?

1/2mv_0^2=1/2kd^2
d=0.84-0.56=0.28
Something wrong here. You need to say there is KE + spring energy initially and at least spring energy finally. Probably final KE as well since it has to hit fast enough to knock over a bottle. How fast is that?

Subtracting d values is not going to give you the same result as subtracting their squares.

You have to find the energy needed to stretch the spring so that the block reaches the bottle. This means the spring must stretch to .084 m.

After finding the k of the spring (what is the relationship between $\omega$ and k and m?) write out the expression for the energy of the system (block+spring) at the point of maximum stretch when the bottle is struck. Write out the expression for energy of the system when the block is launched. How are the two expressions related? (hint:Assume that energy is conserved).

AM

## 1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion in which a system moves back and forth around a stable equilibrium point, with a constant amplitude and a constant period.

## 2. What is a frictionless block problem?

A frictionless block problem is a type of physics problem that involves a block sliding on a surface without any friction. This simplifies the problem and allows for easier calculations and analysis.

## 3. What are the key components of a SHM frictionless block problem?

The key components of a SHM frictionless block problem include the mass of the block, the spring constant of the spring attached to the block, and the displacement of the block from its equilibrium position.

## 4. How do you calculate the period of a SHM frictionless block?

The period of a SHM frictionless block can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass of the block, and k is the spring constant.

## 5. How does the amplitude affect the motion of a SHM frictionless block?

The amplitude of a SHM frictionless block affects the distance that the block travels from its equilibrium position. A larger amplitude will result in a larger displacement, while a smaller amplitude will result in a smaller displacement.

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