A pole of length 1.7m and mass 15kg is supported by two people. A boy of mass 65kg sits 0.75m from one end and a girl of mass 49kg sits 0.5m from the other end. Calculate the forces exerted by the sup

Let $R_M$ be the reaction force from the mother and $R_F$ be the reaction force from the father.
Pole length $L = 1.7$ m.
Weight of pole $W_P = 150$ N, acting at the center of the pole, 0.85 m from each end.
Weight of boy $W_B = 650$ N, sitting 0.75 m from one end (let's assume the mother's end).
Weight of girl $W_G = 490$ N, sitting 0.5 m from the other end (father's end). This means the girl is at $1.7 - 0.5 = 1.2$ m from the mother's end.

Clockwise moments:
Moment due to boy = $W_B \times 0.75 = 650 \text{ N} \times 0.75 \text{ m} = 487.5 \text{ Nm}$
Moment due to pole = $W_P \times 0.85 = 150 \text{ N} \times 0.85 \text{ m} = 127.5 \text{ Nm}$
Moment due to girl = $W_G \times 1.2 = 490 \text{ N} \times 1.2 \text{ m} = 588 \text{ Nm}$
Anticlockwise moment:
Moment due to father's support = $R_F \times 1.7$

Sum of clockwise moments = Sum of anticlockwise moments

Upward forces: $R_M + R_F$
Downward forces: $W_B + W_P + W_G$

Substitute $R_F$:

The reaction of the mother is $R_M$ and the reaction of the father is $R_F$.

8. b) i.
Relative motion describes the motion of an object with respect to another object or a specific frame of reference. It means that the observed velocity or position of an object depends on the motion of the observer.

8. b) ii.
Given: Velocity of car A, $V_A = 100 \text{ ms}^{-1}$. Velocity of car B, $V_B = 60 \text{ ms}^{-1}$.

α. If the two cars are travelling in the same direction:
The relative velocity of car A with respect to car B is the difference between their velocities.

β. If the two cars are travelling in opposite directions:
The relative velocity of car A with respect to car B is the sum of their magnitudes of velocities.

8. c)
Given: Mass $m = 4.0$ kg. Initial velocity $u = 20 \text{ ms}^{-1}$. Final velocity $v = 30 \text{ ms}^{-1}$. Time $t = 5$ s.

i. Acceleration of the body:
Using the equation of motion $v = u + at$:

ii. Work done by the body:
Work done is equal to the change in kinetic energy.

iii. Change in momentum of the body:
Change in momentum $\Delta p = mv - mu$.

9. a)
Two factors that determine the quantity of heat in a body are:

• The mass of the body.
• The specific heat capacity of the material of the body.
• The change in temperature of the body. (Any two of these are sufficient)

9. b)
Given: Mass of lead $m = 100$ kg. Initial temperature $T_1 = 40 \text{ °C}$. Melting point $T_m = 320 \text{ °C}$. Power of furnace $P = 10$ kW $= 10 \times 10^3$ W. Specific heat capacity of lead $c = 120 \text{ Jkg}^{-1}\text{K}^{-1}$. Specific latent heat of fusion of lead $L_f = 2.5 \times 10^4 \text{ Jkg}^{-1}$.

i. Quantity of heat required to heat the lead to its melting point:
The change in temperature $\Delta T = T_m - T_1 = 320 \text{ °C} - 40 \text{ °C} = 280 \text{ °C}$.
Since $1 \text{ °C}$ change is equal to $1 \text{ K}$ change, $\Delta T = 280 \text{ K}$.

ii. Additional heat required to melt the lead:
This is the latent heat of fusion.

iii. Time taken to supply this additional energy:
The power of the furnace is $P = \frac{Q_2}{t}$. We need to find $t$.