Question
A pendulum bob of mass m on a cord of length L is pulled sideways until the cord makes an angle θ with the vertical as shown in the figure to the right. The change in potential energy of the bob during the displacement is:
(A) mgL (1–cos θ) (B) mgL (1–sin θ) (C) mgL sin θ (D) mgL cos θ
▶️Answer/Explanation
Ans:A
Solution: The potential energy at the first position will be the amount “lost” as the ball falls and this will be the change in potential. U=mgh = mg(L–Lcos θ)
Question
A ball is thrown vertically upwards with a velocity v and an initial kinetic energy Ek. When half way to the top of its flight, it has a velocity and kinetic energy respectively of
(A) \(\frac{v}{2}, \frac{E_{k}}{2}\) (B) \(\frac{v}{\sqrt{2}}, \frac{E_{k}}{2}\) (C) \(\frac{v}{4}, \frac{E_{k}}{2}\) (D) \(\frac{v}{2}, \frac{E_{k}}{\sqrt{2}}\)
▶️Answer/Explanation
Ans:B
Solution: Half way up you have gained half of the height so you gained ½ of potential energy. Therefore you must have lost ½ of the initial kinetic energy so E2 = (Ek/2). Subbing into this relationship E2 = (Ek/2)
½ mv22 = ½ m v2/ 2
v22 = v2/ 2 …. Sqrt both sides gives answer
Question
A football is kicked off the ground a distance of 50 yards downfield. Neglecting air resistance, which of the following statements would be INCORRECT when the football reaches the highest point?
(A) all of the balls original kinetic energy has been changed into potential energy
(B) the ball’s horizontal velocity is the same as when it left the kickers foot
(C) the ball will have been in the air one-half of its total flight time
(D) the vertical component of the velocity is equal to zero
▶️Answer/Explanation
Ans:A
Solution: At the top, the ball is still moving (vx) so would still possess some kinetic energy
Question
A fan blows the air and gives it kinetic energy. An hour after the fan has been turned off, what has happened to the kinetic energy of the air?
(A) it disappears (B) it turns into potential energy (C) it turns into thermal energy (D) it turns into sound energy
▶️Answer/Explanation
Ans:C
Solution: Total energy is always conserved so as the air molecules slow and lose their kinetic energy, there is a heat flow which increases internal (or thermal) energy
Question
A rock is dropped from the top of a tall tower. Half a second later another rock, twice as massive as the first, is dropped. Ignoring air resistance,
(A) the distance between the rocks increases while both are falling.
(B) the acceleration is greater for the more massive rock.
(C) they strike the ground more than half a second apart.
(D) they strike the ground with the same kinetic energy.
▶️Answer/Explanation
Ans:A
Solution: Eliminating obviously wrong choices only leaves A as an option. The answer is A because since the first ball has a head start on the second ball it is moving at a faster rate of speed at all times. When both are moving in the air together for equal time periods the first faster rock will gain more distance than the slower one which will widen the gap between them.