I only need help with part a please. As shown below, a crate of mass \( m = 31.4 \) kg is allowed to slide down an incline of \( \theta = 33.0^\circ \).Initially, the crate is in motion with \( v_0 = 1.55 \) m/s and is a distance \( d = 2.44 \) m above a large spring, as measured parallel to the incline. The surface of the incline has friction with \( \mu_k = 0.220 \). The spring at the bottom of the ramp has spring constant \( k = 413 \) N/m. Assume the spring is massless and note that the incline continues to have friction under the spring.(a) What is the maximum compression of the spring?(b) What percentage of the initial mechanical energy of the crate is stored in the spring at maximum compression?(c) What is the magnitude of the acceleration of the crate at the moment when it is sliding down the incline and has compressed the spring to half its maximum compression?(d) What is the maximum speed reached by the crate and at how far is the spring compressed when this maximum speed is reached?**Diagram Explanation:**- The image shows an inclined plane with an angle \( \theta \).- A crate, labeled with mass \( m \), is positioned on the incline.- There is a spring at the bottom of the incline.- The crate’s initial distance from the spring is marked as \( d \).- An arrow indicates the direction of motion down the incline towards the spring.

Given mass of crate m=31.4 kg Distance from spring d=2.44m Initial velocity v=1.55m/s Kinetic…

As shown below, a crate of mass m = 31.4 kg is allowed to slide down an incline of 0 = 33.0°. Initially the crate is in motion with vo = 1.55 m/s and is a distance d = 2.44 m above a large spring, as measured parallel to the incline. The surface of the incline has friction with µk = 0.220. The spring at the bottom of the ramp has spring constant k = 413 N/m. Assume the spring is massless and note that the incline continues to have friction under the spring. (a) What is the maximum compression of the spring?

As shown below, a crate of mass m = 31.4 kg is allowed to slide down an incline of 0 = 33.0°. Initially the crate is in motion with vo = 1.55 m/s and is a distance d = 2.44 m above a large spring, as measured parallel to the incline. The surface of the incline has friction with µk = 0.220. The spring at the bottom of the ramp has spring constant k = 413 N/m. Assume the spring is massless and note that the incline continues to have friction under the spring. (a) What is the maximum compression of the spring?