Turning effect of a force 1 pivot problems 2 pivot problems Moments Turning effect of a force 1 pivot problems 2 pivot problems

Moment of a force Moment is the turning effect of a force. This can be increased by: Increasing the force. Increasing the distance from the force to the pivot

Definition Moment = Force x perpendicular distance from force to pivot m = Fdcosθ

Units Since it is product of force and distance then the unit of moment is Nm or Ncm as appropriate.

Principle of moments For equilibrium The sum of the anticlockwise moments is equal to the sum of the clockwise moments. The net force vertically is zero.

Example Show that this system is in equilibium

acwm = cwm 500 N x 2 m = 1000N x 1 m 1000 Nm = 1000Nm

Example A shelf of width 50 cm and weight 10 N is attached to a wall and supported by a strut 80 cm long. A book of weight 15 N is placed on the shelf so that its centre of mass is 20 cm from the wall. The total moment of the downward forces. The force in the strut.

Total moment clockwise = 15x20 + 10x25 = 550 Ncm Therefore total moment provided by strut is also 550 Ncm Fdsinθ = 550

θ is between the 50 and 80 cm lengths

cos θ = 50/80 θ = 51. 3 degrees Fx50xsin(51. 3) = 550 F = 14 cos θ = 50/80 θ = 51.3 degrees Fx50xsin(51.3) = 550 F = 14.1 N The force in the support strut is 14. 1 N

Two pivot problems Bridge 2 men carrying a ladder

Example A ladder of length 5m and mass 10 kg is carried by two men. A supports the ladder at the left hand end and B supports it 1 m from the right hand end. Find the force each exerts on the ladder (the support forces.)

Diagram is vital

Answer Take moments about A acwm = cwm 10x9.8x2.5 = F(B)x4 = F(B)x4 61.25 N = F(B) F(A) + F(B) = 10x9.8  F(A) = 36.75 N

Torque Turning effect of a pair of forces Cars – peak torque advertised and at a known rev range – more torque = more responsive to throttle dabs. Power is a function of both torque and cycles per unit time.