The total work done by the child as he slides down the plane is 447.25 J.
What is the acceleration of the child?
The acceleration of the child is calculated by applying the concept of Newton's second law of motion.
mgsinθ - Ff = ma
where;
- θ is the angle of inclination of the incline
- Ff is the frictional force
- m is mass of the child
- g is acceleration due to gravity
- a is acceleration of the child
The angle of inclination of the incline is calculated as follows;
sinθ = h/d
sin θ = (1.78 m) / (4.88 m)
sin θ = 0.365
θ = arc sin(0.365)
θ = 21.39 ⁰
mgsinθ - Ff = ma
(32.5 x 9.8) sin(21.39) - 24.6 = 32.5a
91.56 = 32.5a
a = 91.56 / 32.5
a = 2.82 m/s²
The total work done by the child is calculated as follows;
W = Fd
where;
- F is the force of the child
- d is the distance moved
W = ma x d
W = (32.5 x 2.82) x 4.88
W = 447.25 J
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