All Mechanics DOUBTS HERE!!!

[astarmathsandphysics]

Later

[astarmathsandphysics]

those two questions above.

[dk bose]

1)A pile driver of mass 350kg drives vertically a pile of mass 630kg into horizontal ground.the pile driver strikes the pile directly with a speed 7m/s and does not rebound,so that the pile driver and the pile move as one body into the ground.the pile driver and the pile penetrate 0.5m into the ground.Assuming that the force exerted by the ground on the pile and the pile driver during the motion is constant.
(a)calculate in N to 2sf the value of this constant force. 

2)A straight uniform rigid beam AB,of length 6 m and mass 15 kg, is supported at A and B and rests horizontally.A load of mass 60kg is placed on the beam at the point C.Given that the magnitude of the force exerted on the support at A is twice the magnitude of the force exerted on the support at B,find the distance AC.

plzz anyone solve these two sums and post the solutions as fast as possible!!!!!!!

[astarmathsandphysics]

Later

[astarmathsandphysics]

Questions 1 and 2 answered in attachment

[dk bose]

1) A force acts on a particle,where R=(7i+16j)N.the force R is the resultant of two forces P and Q.the line of action of P is parallel to the vector (i+4j) and the line of action of Q is parallel to the vector (i+j).
Determine the forces P and Q expressing each in terms of i and j.

2)At 11:00 hours the position vector of an aircraft relative to an airport O is (200i+30j)km,i and j being unit vectors due east and due north respectively.The velocity of the aircraft is (180i-120j)km/h.find:
(a) how far it is from O at 12:00.

3) this question is quite huge so i cant write it here.it is from heinemann modular mechanics  unit 1 textbook.page no 57.review exercise 1.question no 7,part (f).

Solve all these 3 questions and give the solutions as fast as possible!!!!!

[astarmathsandphysics]

For q3 I don't have the textbook. Can you scan it?

[Becca]

Okay, I have solved the first two questions. I'm doing CIE A levels, so I don't have the book for the last question... and I couldn't find that particular page on the Internet. Drat it. Hope you understand my solutions!

First Question:

P is parallel to (i+4j), so P= x(i+4j)
Q is parallel to (i+j), so Q= y(i+j)

x & y are to be calulated, as follows:
since R is the resultant of P and Q, R = P+Q

therefore,
R = P+Q
(7i+16j) = x(i+4j) + y(i+j)
(7i+16j) = (xi + 4xj) + (yi +yj)
(7i+16j) = [(x+y)i + (4x+y)j]

Hence, based on the above equation, you can say that:
x+y = 7
y=7-x     >>>>>>>>>>>>>>>>> eqn 1

and,
4x+y = 16
y= 16-4x    >>>>>>>>>>>>>>>>>>>eqn 2

Sub eqn 1 into eqn 2:
7-x=16-4x
3x=9
x=3

Sub x=3 into eqn 1
y=7-3
y=4

Therefore, P=x(i+4j)
                P= 3(i+4j)
                P=3i + 12j

and Q=y(i+j)
      Q=4(i+j)
       Q=4i+4j


Second Question:

1 hour passes from 11.00 to 12.00, so the plane moves through a vector of (180i-120j) within this time. The initial vector is (200i+30j).
Therefore, the final vector is:

(200i+30j) + (180i-120j) = (380i-90j)

However, since the question is asking for the distance of the aeroplane from the airport, we must find the magnitude of the above vector via Pythagoras' theorem:

?[380^2+ (-90)^2] = 390.5 km

^For some reason, I couldn't insert the square root sign; it became a '?' instead.

[Becca]

Oh no, I'm sorry, Mr Astarmathsandphysics! When I started writing the reply, you had not replied yet! Sorry again, I didn't notice that you had replied already before I posted mine...

[astarmathsandphysics]

Is ok. If you had posted first I might have posted anyway.

[dk bose]

1)A body of mass 5kg is held in equilibrium under gravity by two inextensible light ropes.One rope is horizontal,the other is at an angle teetha to the horizontal,as shown in the attachment.The tension in the rope inclined at teetha to the horizontal is 72 N.
(a) the tension T in the horizontal rope giving ur ans to the nearest N.

2)A small sphere R,of mass 0.08kg,moving with speed 1.5m/s,collides directly with another small sphere S,of mass 0.12kg,moving in the same direction with speed 1m/s. Immediately after the collision R and S continue to move in the same direction with speeds U m/s and V m/s respectively.
Given that U:V=21:26,
(a) show that V = 1.3,
(b) find the magnitude of the impulse, in Ns, received by R as a result of the collision.

[iluvme]

1)A body of mass 5kg is held in equilibrium under gravity by two inextensible light ropes.One rope is horizontal,the other is at an angle teetha to the horizontal,as shown in the attachment.The tension in the rope inclined at teetha to the horizontal is 72 N.
(a) the tension T in the horizontal rope giving ur ans to the nearest N.

2)A small sphere R,of mass 0.08kg,moving with speed 1.5m/s,collides directly with another small sphere S,of mass 0.12kg,moving in the same direction with speed 1m/s. Immediately after the collision R and S continue to move in the same direction with speeds U m/s and V m/s respectively.
Given that U:V=21:26,
(a) show that V = 1.3,
(b) find the magnitude of the impulse, in Ns, received by R as a result of the collision.

Its been a long time since I did my M1, I did the first question for you, as for the second, :X

[astarmathsandphysics]

my answer to two questions above

[dk bose]

my doubts,the circled ones.!!!

[astarmathsandphysics]

No can do now. Nov exams tomorrow and I have a 24 day ahead. Will do Tues morn