Forces in Equilibrium Problems

Question 1

An object of mass 50kg is suspended by two strings from points A and B as shown below.
a)	Calculate the tension, Te in each of the strings.
b)	If the distance A B is decreased, will the tensions in the strings increase, decrease or stay the same? Explain your answer.

Question 2

A uniform ladder of mass 15kg and length 2·5m is leaning against a smooth wall, as shown below.
a)	Using the principle of moments, calculate the magnitude of the force exerted by the wall on the ladder.
b)	Find the direction of the force exerted by the ground on the ladder.
c)	Calculate the magnitude of the force exerted by the ground on the ladder.

Question 3

A set of uniform shelves is supported by two vertical pieces of wood. The forces exerted by the pieces of wood, in order to support the shelves, are F1 and F2.
a)	If each shelf has a mass of 1·5kg, calculate the magnitudes of the two forces, F1 and F2.
b)	An object of mass m1 = 4kg is placed in the centre of one of the shelves, as shown below.
Calculate the new magnitudes of the forces, F1 and F2.
c)	A second object, of mass m2 = 6kg is now placed half way between the first object and the right hand support, as shown below.
Calculate the new magnitudes of the forces, F1 and F2.

Question 4

A vehicle is crossing a uniform bridge. The distance between the centre of gravity of the vehicle and the end, A, of the bridge is d (see diagram below). The weight of the bridge is W1 = 20000N and the weight of the vehicle is W2 = 7500N. F1 and F2 are the forces exerted by  the supports on  the bridge.

Show that the relation between the magnitude of F1 and the distance, d, is given by

F1 = 23500 - (1500×d)

Question 5

A rock musician (very famous in the 1960’s and 1970’s) made a record inspired by the turning effects of forces in equilibrium.
a)	What was the name of the record and what year was it made?
b)	What was the name of the musician?
c)	Find the names of the other three members of the group he was in when he became famous.