A spring (k = 200 N/m) is fixed at the top of a frictionless plane inclined at angle θ = 39 . A 2.0 kg block is projected up the plane, from an initial position that is distance d = 0.80 m from the end of the relaxed spring, with an initial kinetic energy of 31 J.
(a) What is the kinetic energy of the block at the instant it has compressed the spring 0.10 m?
(b) With what kinetic energy must the block be projected up the plane if it is to stop momentarily when it has compressed the spring by 0.60 m?

Ametal ball with a mass of 0.028 kg is dropped from rest at a height of 1.0 meters above the ground. assuming the energy in the ball is conserved, how much kinetic energy will the ball have when it is 0.5 meters above the ground?

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

This is the substance(s) formed in a chemical reaction.