Problem 5: A block of mass m = 4.5 kg is attached to a spring with spring constant k = 81 N/m. It is initially at rest on an inclined plane that is at an angle of 0 = 28° with respect to the orizontal, and the coefficient of kinetic friction between the block and the plane is ug = 0.19. In th nitial position, where the spring is compressed by a distance of d= 0.18 m, the mass is at its lowes position and the spring is compressed the maximum amount. Take the initial gravitational energy o he block as zero.

Problem 2: An object of mass M is hanging from a spring (with I_o =0 and a spring constant k). There is a constant force from the wind, F_wind, blowing to the right, so the mass is initially at rest, but hanging at an angle Theta from the vertical because of the presence of the wind. Suddenly, spring breaks, and the mass drops under the influence of F_wind (note F_air and F_wind are the same constant vector!) and its weight. If the object (in equilibrium before the spring breaks) is a height H above the ground, how far laterally (in the direction of the wind) does the object hit the ground, L (given theta, k, M, g, H)?

A warehouse worker is pushing a 90.0 kg crate with a horizontal force of 283 N at a speed of v = 0.875 m/s across the warehouse floor. He encounters a rough horizontal section of the floor that is 0.75 m long and where the coefficient of kinetic friction between the crate and floor is 0.354. (a)Determine the magnitude and direction of the net force acting on the crate while it is pushed over the rough section of the floor. (b) Determine the net work done on the crate while it is pushed over the rough section of the floor. (c) Find the speed of the crate when it reaches the end of the rough surface.

A block of mass m is located on an inclined plane that makes an angle with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is μ₁. The block presses against, but is not attached to, a spring with constant k₁. When the spring is at its equilibrium position, the block is at a height h above the ground, as shown. The initial position of the block, from which it is released, is a bit further up the inclined plane such that the spring is initially compressed by Ax. At the bottom of the inclined plane is a horizontal plane with a different coefficient of friction, μ2, for the first distance, d, after which the surface is frictionless, and the equilibrium position of a spring with constant k₂ is encountered. Part (a) Suppose that numeric values are such that block comes to rest before reaching the the ramp. Let x distance traveled from the equilibrium position of the block towards the bottom of the ramp. Enter an expression for x. Part (b) Suppose…