A 197-g block is pressed against a spring of force constant 1.42 kN/m until the block compresses the spring 10.0 cm. The spring rests at the bottom of a ramp inclined at 60.0 to the horizontal. Using energy considerations, determine how far up the incline the block moves from its initial position before it stops under the following conditions. (a) if the ramp exerts no friction force on the block (b) if the coefcient of kinetic friction is 0.380 Part 1 of 5 - Conceptualize Part of this problem describes a situation that can be duplicated in a laboratory experiment. We expect a distance of a few meters if the ramp exerts no friction and perhaps half the distance if we consider force due to friction. Pan 2 of 5 - Categorize We must compute the spring energy before and after launch. We will use the nonisolated system energy model to be sure that we keep track of the energy from all of the sources. an 3 of 5 - Analyze We consider gravitational energy, elastic energy, kinetic energy, and internal energy. The spring is initially compressed by x, = 0.100 m. The block travels up the ramp a distance L1. The work that the spring does on the block is given by the following equation. 1 1 1 w5 = 3/04 a 31ml = 3ka , o 1 : kxi2. 2 Gravity does work on the block specied in the equation below. There is no friction. Wg = rngd cos(90" + \") a mgd sin( ) (a) Since we know W5 + W = 0, and Z W = AK, we have %kx,2 mgd sin( ) = D, and substitution gives 1 3 2 E( x 10 N/m)( m) = (l jkg)(9.80 m/52)d sin l j", Solving the above equation for d, we nd that the distance up the incline the block would travel in the absence of friction is d=l:m