Scie 1001
Question 1
Question 2
Question 3
Question 4

 

 

Questions and Answers

ladder

2. A strongman is demonstrating his strength by pulling a horizontal rope attached to a wrecking ball of weight 2000N suspended from a crane. At maximum effort, the man is able to deflect the suspending cable at an angle of 60° to the horizontal.
(a) Draw a diagram to represent the forces.
(b) calculate the tension on the cable T1.
(c) Calculate the strength of the man.

 

Fig 1
Answer  
ladder
(a)

ladder

(b) The force T1 can be resolved into two forces at right angles to each other T1h and T1v.

Recall Sin θ = opposite/hypotenuse
and Cos θ = adjacent/hypotenuse

so Sin 60° = T1v/T1 -----Eq 1

and Cos 60° = T1h/T1 --- Eq2

From Eq1 T1 = = T1h/Cos 60° --- Eq3

From Eq2 T1 = T1v/Sin 60° --- Eq4
Fig 2  
ladder
Figure 2 can be redone to show the components of Fg (Fv and Fh)

The ladder is in equilibrium:
Recall from Newton's First and Second Laws the conditions for static equilibrium:

∑F = 0
∑Horizontal forces = 0 --- Eq5
∑Vertical forces = 0
--- Eq6



Fig 3

From Eq6
T1v + W = 0
T1v = -W
Taking up as positive
T1v = -(-2000N)
T1v = 2000N up

(d) From Eq4
T1 = = T1v/Sin 60°

T1 = 2000N/Sin 60°

T1 = 2310N


(c) From Eq3
T1 = T1h/Cos 60°

T1 Cos 60° = T1h
T1h = 1155N

From Eq5
T2 + T1h = 0
T2 = -T2

Taking to the right as positive
T2 = -(-1155N)
T2 = 1155N

Answers:
(a)

Double Checks for the answers Fg, Fv and Fh.
By Pythagoras:

T1h2 + T1hFv2 = T12

11552 + 20002 = 23102

 

 

ladder

 

 

 

 

 

 

(b) T1 = 2310N (to the right )
(c) T2 = 1155N (to the left)
   
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Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.