1. Work done by spring = 0.279 Joules 2. Work lost due to friction = 0.716 Joules 3. Speed of block when first hit spring = 0.680 m/s 1. Using Hooke's law, the potential energy stored in the spring is E = 0.5kx^2 where E = potential energy k = spring constant x = distance the spring is deformed. Substitute the known values into the formula E = 0.5 223 N/m (0.05 m)^2 E = 111.5 N/m 0.0025 m^2 E = 0.27875 Nm E = 0.27875 (kg m)/s^2 m E = 0.27875 (kg m^2)/s^2 E = 0.27875 J Rounding to 3 significant figures gives 0.279 Joules. 2. The amount of force needed due to kinetic friction is F = k * Fn where k = coefficient of friction Fn = Normal force The normal force is the mass of the object multiplied by the gravitational acceleration so, 4.3 kg * 9.8 m/s^2 = 42.14 (kg*m)/s^2 Now multiply by the coefficient of friction, getting 42.14 (kg*m)/s^2 * 0.340 = 14.3276 (kg*m)/s^2 = 14.3276 N So we have 14.3276 N over a distance of 5 cm (0.05m), so 14.3276 N * 0.05 m = 0.71638 Nm = 0.71638 J Rounding to 3 significant figures gives 0.716 Joules 3. The total work done on the block is the work used to compress the spring plus the work lost due to friction, so 0.279 J + 0.716 J = 0.995 J Now the energy of a moving object is expressed as the following equation. E = 0.5 M V^2 where E = Energy M = Mass V = Velocity. So setting energy equal to the amount used to stop the mass, we get 0.995 J = 0.5 M V^2 0.995 (kg*m^2)/s^2 = 0.5 M V^2 Substituting the known mass, getting 0.995 (kg*m^2)/s^2 = 0.5 4.3kg V^2 0.995 (kg*m^2)/s^2 = 2.15 kg V^2 And solve for V 0.995 (kg*m^2)/s^2 = 2.15 kg V^2 0.462790698 m^2/s^2 = V^2 0.680287217 m/s = V And finally, round to 3 significant figures, getting 0.680 m/s