Amass m is pressed against a horizontal ideal spring with spring constant k. it is not actually attached, so that when the spring is no longer pressing on the mass, the mass separates from the spring.

for parts (a) and (b), assume that the surface on which the mass travels is frictionless.
(a) how far must the spring be compressed for the mass to have a speed v1 when it is at the equilibrium point of the spring?
(b) at what point in the motion does the mass leave the spring (hint: consider the spring force)?

for parts (c) through (d), assume there is a coefficient of friction µk between the block and the surface.
(c) how far must be the spring now be compressed for the mass to have the same velocity v1 when it is at the spring’s equilibrium point? (d) how far beyond the equilibrium point will the mass travel before coming to rest?

Which seasons are the northern and southern hemispheres experiencing in the image? it is summer in both the northern and southern hemispheres. it is summer in the northern hemisphere and winter in the southern hemisphere. it is winter in both the northern and southern hemispheres. it is winter in the northern hemisphere and summer in the southern hemisphere.

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 ⇒

Sound is a disturbance that travels through a medium as a