物理動量 DSE、CE 選擇題

1.

Trolleys P and Q on a smooth track with a compressed spring between them

On a horizontal smooth track, two trolleys $P$ and $Q$ are held at rest with a light compressed spring in between as shown in the above figure. The masses of $P$ and $Q$ are $m$ and $2m$ respectively. When the trolleys are released and separate, trolley $Q$ moves to the right with speed $v$ . Which of the following statements are correct ?

(1)After separation, the total momentum of the two trolleys is

4mv

.

(2)After separation, the kinetic energy of trolley

P

is twice that of trolley

Q

.

(3)The energy initially stored in the compressed spring is at least

3mv^2

.

2.

An egg will probably break if it is released at a height and lands on a hard surface. However, the egg may not break if it is released at the same height but lands on a soft cushion. It is because, when the cushion is used,

3.

Ball A (6 m/s to the right) and ball B (4 m/s to the left) approaching each other

Ball $A$ and ball $B$ of masses $2$ kg and $1$ kg respectively collide head-on as shown above. Which of the following diagrams show(s) the possible result(s) after the collision ?

Three diagrams (1) to (3) showing velocities of A and B after collision

4.

Block sliding to the right towards a vertical wall on a horizontal smooth surface

A block slides along a horizontal smooth surface as shown in the figure above. It collides with a vertical wall and rebounds along its original path. Which of the graphs below best shows the variation of its momentum $p$ with time $t$ ?

Four graphs A to D of momentum p against time t

5.

In an explosion, an object is blown into $2$ pieces, $A$ and $B$ , which fly off in opposite directions. The mass of $A$ is $0.3$ kg. The graph shows the variation of velocity of $A$ and $B$ with time before and after the explosion. What is the mass of $B$ and the estimated magnitude of the average net force acting on $B$ during the explosion ?

Velocity-time graph: A rises from 0 to 3 m/s and B falls from 0 to -1 m/s between t = 0.05 s and t = 0.25 s

	Mass of $B$	Average net force acting on $B$
	$0.1$ kg	$0.4$ N
	$0.1$ kg	$0.5$ N
	$0.9$ kg	$3.6$ N
	$0.9$ kg	$4.5$ N

6.

Trolleys $A$ and $B$ of masses $m_A$ and $m_B$ respectively travel along a horizontal road in opposite directions as shown.

Trolley A moving right and trolley B moving left on a horizontal road

Later they make a head-on inelastic collision and stick together. The graph below shows the velocity-time relationship of the two trolleys before and after the collision.

Velocity-time graph: A at 4 m/s and B at -1 m/s until 4 s, then A and B together at 2 m/s

(Ignore the collision time and the friction acting on the trolleys.) What is the ratio $m_A : m_B$ ?

7.

A body initially at rest, is exploded into two parts. Which of the following correctly describes the change in total momentum and total kinetic energy ?

	Total momentum	Total kinetic energy
	increases	increases
	increases	remains unchanged
	remains unchanged	increases
	remains unchanged	remains unchanged

8.

Tom and John stand on two trolleys of negligible masses. Both boys are initially at rest and Tom holds a ball of $3$ kg. The masses of Tom and John are $30$ kg and $27$ kg respectively. After Tom has thrown the ball to John, Tom moves backwards with a speed of $1\ \mathrm{m\,s^{-1}}$ . What is the speed of John after he has caught the ball ?

Tom (moving left at 1 m/s) and John on trolleys with the ball travelling from Tom to John on smooth ground

9.

An electric fan is installed at one end of a trolley and a card is fixed at the other end with the plane of the card facing the fan. What happens to the trolley when the electric fan is turned on ?

Trolley with an electric fan at the right end and a card at the left end; air flow arrow pointing left; trolley on the ground

10.

A car $P$ of mass $1000$ kg moves with a speed of $20\ \mathrm{m\,s^{-1}}$ and makes a head-on collision with a car $Q$ of mass $1500$ kg, which was moving with a speed of $10\ \mathrm{m\,s^{-1}}$ in the opposite direction before the collision. If the two cars stick together after the collision, find their common velocity immediately after the collision.