Certainly! Let's break down the problem step-by-step and solve it:
### Given:
- Mass of the boy, [tex]\( m \)[/tex] = 40 kg
- Height of the roof, [tex]\( h \)[/tex] = 8 m
- Time taken, [tex]\( t \)[/tex] = 5 s
- Acceleration due to gravity, [tex]\( g \)[/tex] = 10 m/s²
### (i) The Force of Gravity Acting on the Boy:
The force of gravity acting on an object (weight) is calculated using the formula:
[tex]\[ F = m \times g \][/tex]
Where:
- [tex]\( F \)[/tex] is the force of gravity
- [tex]\( m \)[/tex] is the mass
- [tex]\( g \)[/tex] is the acceleration due to gravity
So:
[tex]\[ F = 40 \text{ kg} \times 10 \text{ m/s}^2 = 400 \text{ N} \][/tex]
The force of gravity acting on the boy is 400 N (Newtons).
### (ii) The Work Done by Him Against the Force of Gravity:
The work done against gravity when lifting an object is calculated using the formula:
[tex]\[ W = F \times d \][/tex]
Where:
- [tex]\( W \)[/tex] is the work done
- [tex]\( F \)[/tex] is the force
- [tex]\( d \)[/tex] is the distance (height in this case)
Substituting the values, we get:
[tex]\[ W = 400 \text{ N} \times 8 \text{ m} = 3200 \text{ J} \][/tex]
The work done by the boy against the force of gravity is 3200 J (Joules).
### (iii) The Power Spent by the Boy:
Power is the rate at which work is done and is calculated using the formula:
[tex]\[ P = \frac{W}{t} \][/tex]
Where:
- [tex]\( P \)[/tex] is the power
- [tex]\( W \)[/tex] is the work done
- [tex]\( t \)[/tex] is the time taken
Substituting the values, we get:
[tex]\[ P = \frac{3200 \text{ J}}{5 \text{ s}} = 640 \text{ W} \][/tex]
The power spent by the boy is 640 W (Watts).
### Summary:
- The force of gravity acting on the boy is 400 N.
- The work done by him against the force of gravity is 3200 J.
- The power spent by the boy is 640 W.
