A spring is used to stop a 50-kg package which is moving down a 20º incline. The spring has a constant k = 32 kN/m and is held by cables so that it is initially compressed 50 mm. Knowing that the velocity of the package is 2 m/s when it is 8 m from the spring and neglecting friction, determine the maximum additional deformation of the spring in bringing the package to rest.

Explanation:

The system formed by the spring and the package is described by the means of the Principle of Energy Conservation:

After expanding and symplifying the expression, a second-order polynomial is found:

The roots of the polynomial are:

Physically speaking, the first root is the only real solution.

weather forecasts are done by collecting data about the current state of the atmosphere mainly the temperature, humidity and wind and using meteorology, to determine the atmosphere that evolves over time. the h and l mean the high and low pressure. the red strip is a warm front. the blue strip is a cold front. the blue and red strip is a stationary front. the purple strip is a occluded front.

explanation: