x Turn on thread page Beta
 You are Here: Home >< Maths

# Mechanics question watch

1. A uniform ladder has a length of 5m and a mass of 20kg. It leans against a smooth vertical wall, with one end on rough horizontal ground. The angle between the ladder and the ground is 70 degrees. A child of has 40kg, is at the top of the ladder. The coefficient of friction between the ladder and the ground is U(weird U).

A) draw a diagram to show the forces acting on the diagram.
B) Show that the magnitude of the friction force acting on the base of the ladder is approximately 178N.

how the heck do i do B and is A right?
Iv been stuck on B for half an hour now .

My A (is it correct?):
Attached Images

2. black line= wall, blue= ladder
3. friction = coefficient of friction x resistance force
so friction = U x R

i am working this out slowly, hang on...
4. Your R isnt 60, i dont think

either
R = 40cos70
or
R - 40 sin70

i dont know i need to revise this stuff, dont i
5. yep but they dont tell you the coefficant so you cant do F= U x R
6. (Original post by vixen23)
friction = coefficient of friction x resistance force
so friction = U x R

i am working this out slowly, hang on...

A value of U has not been given...

OP simply take moments about the base of the ladder to find S.

Resolve forces horizontally and set equal to zero.... this should lead to F=S...

job done..
7. (Original post by vixen23)
Your R isnt 60, i dont think

either
R = 40cos70
or
R - 40 sin70

i dont know i need to revise this stuff, dont i

R should be 60g

and the 2 forces downwards should be 20g and 40g respectively..
8. you need to equate the clockwise and anticlockwise moments. I did it about the foot of the ladder.
5*S*Sin70=5*40g*Cos70 + 2.5*20g*Cos70
so 5*S*Sin70=250g*Cos70
this makes S=250g/(5*tan70)=about 178 (i've forgotten what 1/tan is, it might be sec)

And since S=F then F=178N
9. so when your equateing clockwise, its sin and anti clockwise its cos?

thats the bit that messed me over, and is my part A right?

Thanks so much
10. how did you get cos70 for 40 and 20kg?
11. Regarding your diagram, 2 points:

I think you ought to have the ground there as well.

20 and 40 are not forces. There are masses. The forces would be 20g Newtons and 40g Newtons.

As for the cosines and sines:

The moment of a force is the the product of the magnitude of the force and the perpendicular distance of the line of action of that force from the point about which you are taking moments.

For example the 40kg child.
The force will be 40g Newtons.
The line of action of the force, is simply the line running through the arrow which shows the direction of the force, and you want the perpendicular distance between that line and the base of the ladder. I.e. you want the distnce from the ladder to the wall. Hence the distance is 5 times cos 70, and the moment due to the child is 40g x 5 x cos 70.
12. I dont get it. to get cos its the angle from 40g turning to the ladder line which is 20 degrees?
and S going to the ladder line would be cos 70 or sin 20 to the perpendicular line to the ladder.

I just cant see how to get cos70
13. (Original post by uxa595)
so when your equateing clockwise, its sin and anti clockwise its cos?

thats the bit that messed me over, and is my part A right?

Thanks so much
here's a diagram with the angles added.

in this situation I used sin70 for the clockwise moment since I was trying to find the opposite side of my little angle triangle (opposite=hyp*sin(theta)). whereas in the anticlockwise moments I used cos70 since I needed the adjacent side of my triangle (adjacent=hyp*cos(theta)). I could have used cos 20 for my clockwise moment, but it isn't as tidy when forming tan out of sin/cos.

and as for part A, you need to put g on all your numbers, and the diagrams tend to have a floor. but the values are correct
14. Thanks, i get it now

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: September 27, 2010
Today on TSR

### Boyfriend slept with someone else

...we were on a break

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams