Two cyclists, who weigh the same and have identical bicycles, ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that has a lower grade. Joe gets to the top before Bob. Which statement is true? A) Ignoring friction and wind resistance, Bob and Joe exerted the same amount of work, and the average power of each cyclist was also the same.
B) Ignoring friction and wind resistance, the amount of work done by Joe is equal to the amount of work done by Bob, but the average power exerted by Joe is greater than that of Bob.
C) Ignoring friction and wind resistance, the average power exerted by Bob and Joe was the same, but Joe exerted more work in getting there.
D) Ignoring friction and wind resistance, the amount of work done by Joe is greater than the amount of work done by Bob, and the average power exerted by Joe is greater than that of Bob.

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 ⇒

Two carts, one of mass 2m and one of mass m, approach each other with the same speed, v. when the carts collide, they hook together. assume that positive momentum is to the right. which graph best represents the momentum of both carts over time, before and after the collision?

What is the kinetic energy of a baseball moving at a speed of 40 m/s if the baseball has mass of 0.15 kg?