物理功、能和功率 DSE、CE 選擇題（第 6 頁）

51.

The figure shows a trolley of mass $1$ kg being released from rest from point $X$ of a rough slope. Its speed at $Y$ is $3\ \mathrm{m\,s^{-1}}$ . What is the loss in energy by the trolley when it is moving from $X$ to $Y$ ? (Take $g = 10\ \mathrm{m\,s^{-2}}$ .)

Trolley at X on a rough slope, 1 m above the level of Y

52.

Mass M on a smooth table connected over a pulley to hanging mass m

The figure above shows a mass $m$ connected to another mass $M$ by a string passing over a smooth pulley. The system is moving freely under gravity. Assuming that the table is smooth, which of the following statements is/are correct ?

(1)

m

and

M

move with the same acceleration in magnitude.

(2)The loss in potential energy of

m

is equal to the gain in kinetic energy of

M

.

(3)If the mass of

M

is doubled, its acceleration is halved.

53.

The figure shows a smooth inclined plane with $Y$ being midway between $XZ$ . Two particles $A$ and $B$ of the same mass are released from rest at $X$ and $Y$ respectively. Which of the following statements about $A$ and $B$ is/are true ?

(1)The time required for

A

to reach

Z

is double that for

B

to reach

Z

.

(2)The potential energy for

A

at

Z

is double that for

B

at

Z

.

(3)The kinetic energy for

A

at

Z

is double that for

B

at

Z

.

Smooth inclined plane XZ with particle A at X and particle B at the midpoint Y

54.

An escalator is said to be able to carry $120$ passengers to a height of $10$ m in one minute. Assuming each passenger has a weight of $500$ N, the possible power output by the escalator must be at least

55.

An object is projected vertically upwards. Which of the graphs below correctly describes the variation of its kinetic energy ( $KE$ ) with height ( $h$ ) ?

Four graphs A to D of KE against height h

56.

An object is projected vertically upwards. Which of the graphs below correctly describes the variation of the kinetic energy $E$ of the object with height $h$ ?

Four graphs A to D of kinetic energy E against height h

57.

A block is moving with uniform velocity along a rough horizontal plane. Which of the following statements is/are true ?

(1)The kinetic energy of the block is increasing.

(2)The potential energy of the block is increasing.

(3)The resultant force acting on the block is zero.

58.

A diver jumps up at $A$ from a high platform into water at the point $B$ as shown. The diver descends to $C$ and then floats up to the water surface. Assume that the potential energy at point $B$ is taken to be zero. Which of the following statements is/are true concerning the diver at point $C$ ?

(1)The kinetic energy of the diver is at a maximum.

(2)The kinetic energy of the diver is at a minimum.

(3)The sum of the kinetic energy and potential energy of the diver is zero.

Diver path from platform A, down through water surface B to the lowest point C

59.

The difference in water temperature between the top and the bottom of a waterfall is $0.15^\circ\mathrm{C}$ . Assuming no heat is lost from the water to the surroundings, what is the height of the waterfall ? (The specific heat capacity of water is $4200\ \mathrm{J\,kg^{-1}\,{}^\circ C^{-1}}$ .)

60.

A cannon ball is fired so that it hits the wall at the top of a $10$ m tower. If the energy needed to destroy the wall is $49000$ J and the mass of the cannon ball is $10$ kg, the minimum initial velocity of the cannon ball required to break the tower wall is