# Exam Coming Up: Need Help With Vectors

1. Nov 18, 2004

OK I've been given a past paper for revision for this years physics exam (I'm 14). There are 3 question I need help with working out Here are the questions

1. Two tugs are pulling on a ship with forces of 1500kgf and 2000kgf respectively, each at angle of 45 degress to the longitudal axis of the ship. Calculate the resultant (magnitude and direction), relative to the larger force.
The thing I need help with is constructing the vector diagrams from the coplanar force diagrams, what forces go where

2. A volkswagen campervan of mass 1.3 tonne is being raised for servicing on a hydraulic hoist in a service station. The diameter of the large piston in the hydraulic system below the vehicle is 24 cm and that of the small piston in the driving cylinder is 2.1cm
(a) With no load on the hoist the pressure in the oil in hydraulic system is approximately atmospheric. When the VW is being supported what is the resulting increase in oil pressure?
(b) What force is being exerted by the small piston on the oil in the driving cylinder?
(c) How far does the vehicle rise when the driving piston moves in 17cm?
I only need help with part (c)

3. A boggedcar is winched out by 2 chains of equal length attached to some point on the car. The chains may withstand a maximum tension of 5 tonne force. Will they overcome the resistance of 70kN if the angle between them is 90 degrees?
Again I don't know how to construct a vector diagram from the info given.

Thanks and hope you can help!

2. Nov 18, 2004

Bump, Come on, I'm sure there are plenty who can help me!

3. Nov 19, 2004

4. Nov 19, 2004

### cepheid

Staff Emeritus
Ok, for the first question...did you draw a diagram of the situation? (not a vector diagram per se, but the boat, tugs, ropes etc.)

Assuming the two tugs are on opposite sides of the boat, you have one rope coming out at 45o to the longitudinal axis, and the other coming out at 45o in the other direction (i.e. the ropes are at a right angle). So think about it...the tugging force of each tugboat acts along the rope, so your two force vectors are naturally arranged with their tails together (attached at the centre line of the boat) and the arrows diverging from it. Now, to perfrom vector addtion as usual, slide on of the vectors until it's tip meets the tail of the other. So before the angle between the vectors was 90o. Now the angle between them is 180o - 90o = 90o. Now can you solve? Can you use this method to solve the other problems as well?

5. Nov 19, 2004

Cheers man. Thanks for that, I'll be able to do 1 and 3 now. Do you think you can help with 2(c), I'm having some trouble with it.

6. Nov 21, 2004

BUMp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

7. Nov 21, 2004

### Astronuc

Staff Emeritus
In a hydraulic system, assuming incompressible fluid, the pistons must displace equal volumes, and the volume displaced is simply the stroke x cross-sectional area.

Vol = $$\frac{\pi}{4}d^2h$$, where h is stroke and d=diameter.

d1, d2 and h1 are given, so find h2.