- #1

Wen

- 44

- 0

Questions:

1)

A particle moves along a straight line ABC with B

being the midpoint between A and C. The acceleration

of the particle from A to B is constant at a1, while

its acceleration from B to C is constant at a2. Given

that

vB = (vA + vC) / 2

where vA, vB and vC are the velocities of the particle

at points A, B and C respectively, compare the

magnitudes of a1 and a2.

2)

Two points A and B are a distance s apart along a

straight line. Distance s is divided into n equal

sections, such that each section is a distance s/n

long. A stationary particle starts traveling from A

such that its inital acceleration is a constant a

along the first section. At the end of each section,

the acceleration of the particle increases by a/n,

until the particle moves past B. Find the velocity vB

of the particle after it has moved past point B.

3)

Problem 1

A particle traveled half of a certain distance with a

velocity v0. The remaining part of the distance was

covered with velocity v1 for half the time, and with

velocity v2 for the other half of the time. Find the

mean velocity of the particle over the entire distance

travelled?

Problem 2

A uniform ladder of mass m1 and length 2l rests

against a smooth vertical wall with the foot of the

ladder placed on a rough horizontal floor some

distance away from the bottom of the wall. The

coefficient of static friction between the foot of the

ladder and the floor is ?, and a man of mass m2 climbs

a distance l1 up the ladder from the bottom.

(a) If the ladder makes an acute angle ? with the

floor, how far can the man climb without the ladder

slipping?

(b) If the man is to climb a distance l2 from the foot

of the ladder, what angle should the ladder make with

the horizontal floor?

4)

boat is rowed from A across the river. If the boat is

always pointing in the direction perpendicular to the

river, it will eventually reach C on the opposite bank

in 10 min. If the rower wants to reach point B

directly opposite A instead, he has to point his boat

in the direction towards D when he set off from A, and

maintain that direction as he rows across. In this

case he will take 12.5 min to cross the river.

Given that BC is 120 m, find

(a) the boat's speed v relative to the river;

(b) the river's width L;

(c) the speed u of river flow; and

(d) the angle ? between AD and AB.

5)

Problem 1

A boat can travel at a speed of 3 m s-1 on still

water. A boatman wants to cross a river whilst

covering the shortest possible distance. In what

direction should he row with respect to the bank if

the speed of the water is

(i) 2 m s-1,

(ii) 4 m s-1?

Assume that the speed of the water is the same

everywhere.

Problem 2

The suspension springs of all four wheels of a car are

identical. By how much does the body of a car

(considered rigid) rise above each of the wheels when

its right front wheel is parked on an 8-cm-high

pavement? Does the result change when the car is

parked with both right wheels on the pavement? Does

the result depend on the number and positions of the

people sitting in the car? :grumpy: