Edexcel IAL Maths M1.6.1 Moments of Forces

[Maximum number: 10]

Figure 4

A beam AB has mass 30 kg and length 3 m.
The beam rests on supports at C and D where $A C=0.4 \mathrm{~m}$ and $D B=0.4 \mathrm{~m}$ , as shown in Figure 4.

A person of mass 55 kg stands on the beam between C and D.
The person is modelled as a particle at the point P, where C P=x metres and 0<x<2.2

The beam is modelled as a uniform rod resting in equilibrium in a horizontal position.
Using the model,

(a)

show that the magnitude of the reaction at C is (686-245 x) N.

The magnitude of the reaction at C is four times the magnitude of the reaction at D.
Using the model,

[ 3 ]

M(D)
$\left(R_{C} \times 2.2\right)=55 g(2.2-x)+30 g(1.1)$

M1A1

$\left(R_{C}\right)=(686-245 x)(\mathrm{N}) *$

A1 *

N.B. The M mark here is not available if they use $R_{C}=4 R_{D}$ to
obtain the given result.

(3)

(b)

find the value of x

The person steps off the beam and places a package of mass $M \mathrm{~kg}$ at A.
The package is modelled as a particle at the point A.
The beam is now on the point of tilting about C.
Using the model,

[ 4 ]

$R_C=4R_D$ $R_C+R_D=55g+30g,\qquad \frac54(686-245x)=55g+30g$
or a relevant moments equation eliminating $R_C$ and $R_D$ .
x=0.08
(4)

(c)

find the value of M

[ 3 ]

$\mathrm{M}(C):\qquad Mg(0.4)=30g(1.1)$ M=83
or 82.5 or $\frac{165}{2}$ .
(3)

Edexcel A-Level Mathematics AS M1.6.1 Moment of a Force Questions

Exam points

Edexcel A-Level Mathematics AS M1.6.1 Moment of a Force Questions question 1

Question (a)

Question (b)

Question (c)