物理力矩 DSE、CE 選擇題

1.

Figure (a): uniform plank, 1 m long, hung by two spring balances P and Q at its ends. Figure (b): balance P moved 0.25 m towards Q

Figure (a) shows a uniform plank supported by two spring balances $P$ and $Q$ . The readings of the two balances are both $150$ N. $P$ is now moved $0.25$ m towards $Q$ (see Figure (b)). Find the new readings of $P$ and $Q$ .

	Reading of $P$ / N	Reading of $Q$ / N
	$100$ N	$200$ N
	$150$ N	$150$ N
	$200$ N	$100$ N
	$200$ N	$150$ N

2.

Uniform rod hung by two spring balances P and Q: P is 0.2 m from the left end, 0.5 m between P and Q, Q is 0.3 m from the right end

A uniform rod of weight $50$ N is supported by two spring balances $P$ and $Q$ and remains at rest as shown above. Assume the weight of the rod acts through its mid-point. Find the readings of $P$ and $Q$ .

	Reading of $P$	Reading of $Q$
	$17$ N	$33$ N
	$20$ N	$30$ N
	$30$ N	$20$ N
	$33$ N	$17$ N

3.

A block is initially at rest on smooth horizontal ground. Two forces of equal magnitude $F$ act on the block. In which of the below cases will the block remain at rest ?

Three cases of a rectangular block seen from above with two forces F: (1) forces along parallel lines in opposite directions, (2) forces along the diagonal in opposite directions, (3) forces along parallel lines in the same direction

4.

Uniform plank on two trestles X and Y, with 1.5 m overhang at each end, 5 m between the trestles, weight 450 N at the middle and a worker standing at the right end

A uniform plane of weight $675$ N stands at one end of the plank as shown above. The worker holds a light basket which contains several packets of goods each of weight $6$ N. What is the maximum number of packets he can hold without tilting the plank ?

5.

Weighing device: rod AB held by a string at X, an object hanging at end A and a counter-weight hanging on the rod

A company intends to produce a kind of weighing device as shown. The device is held at point $X$ . The position of the counter-weight is adjusted until the rod $AB$ becomes horizontal. The weight of the object can be read from the scale calibrated on $AB$ . Which of the following changes can increase the maximum weight that can be measured by the device ?

(1)moving the string at

X

towards

A

(2)increasing the mass of the counter-weight

(3)increasing the length of the string from which the counter-weight hangs

6.

Uniform rod of length L pivoted at a point L/4 from one end, with a 14 N downward force at the near end and 3 N downward at the far end

A uniform rod of length $L$ is pivoted at a point $\frac14L$ from one of its ends. Two forces $14$ N and $3$ N act on its two ends as shown above. If the rod is in equilibrium, find the weight of the rod. (Assume the weight of the rod acts through its midpoint.)

7.

A uniform beam of length $3$ m and weight $300$ N lies on a horizontal ground. What minimum vertical force must be applied to one end of the beam to just lift that end off the ground ? (Assume the weight of the beam acts through its mid-point.)

8.

Light plank on trestles S1 and S2: 0.25 m from the left end to S1, 1.25 m between the trestles, 0.5 m from S2 to the right end, with a boy at the mid-point

A light plank of length $2$ m rests on two trestles $S_1$ and $S_2$ as shown in the figure. A boy of weight $500$ N stands at the mid-point of the plank. Find the forces acting on the two trestles by the plank.

	Force acting on $S_1$	Force acting on $S_2$
	$166\frac23$ N	$333\frac13$ N
	$200$ N	$300$ N
	$250$ N	$250$ N
	$300$ N	$200$ N

9.

Uniform plank AB resting on two trestles 1 m from each end and 3 m apart, weight 200 N at the middle, a boy standing at end B

A uniform plank $AB$ of weight $200$ N rests on two trestles as shown above. A boy stands at the end $B$ of the plank. What can be the maximum weight of the boy be without tilting the plank ? (Assume the weight of the plank acts through its centre.)

10.

Light rod PQRST with points 10 cm apart: 2 N downward at R and 2 N upward at T

The above diagram shows a light rod under the action of two vertical forces. Under which of the following conditions will the rod be in equilibrium ?