A chair of weight 110 N lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of F = 45.0 N directed at an angle of 41.0 ∘ below the horizontal and the chair slides along the floor.1)Using Newton's laws, calculate n, the magnitude of the normal force that the floor exerts on the chair.

Find the volume of the ellipsoid x^2+y^2+5z^2=36.

The chart shows the costs and shipping times for materials that a company needs to build a new product. which describes the best trade-off if the company needs to start building their product within the next two years? they should order the domestic materials because it is always best to choose the fastest shipping time. they should order the imported materials because it is always best to choose the lowest cost for materials. since the shipping time is longer, they should order the domestic materials because the additional cost is worth it to get the materials in time. even though the shipping time is longer, they should order the imported materials because they are less expensive and should arrive in plenty of time to build the product.

Aspring is used to stop a 50-kg package which is moving down a 20º incline. the spring has a constant k = 30 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.