Answer:
a) Eg = 3,060.72 j
b) Ek = 2,080 j
c) Etotal = 5,140.72 j
d) Eg = 5,140.2 j
Ek = 0 j
Etotal = 5,140.2 j
Step-by-step explanation:
The given parameters of the person riding the skateboard are;
The mass of the person, m = 65 kg
The height of the person (above ground level), h = 4.8 m
The speed at which the person is traveling, v = 8.0 m/s
a) The gravitational potential energy, Eg = m·g·h
Where;
m = The mass of the object at the given height = 65 kg
g = The acceleration due to gravity, g ≈ 9.81 m/s²
h = The height by which the object is elevated = 4.8 m
∴ Eg = 65 kg × 9.81 m/s² × 4.8 m = 3,060.72 joules
The gravitational potential energy, Eg = 3,060.72 J
b) The kinetic energy, Ek, is given as follows;
Ek = 1/2·m·v²
Where;
v = The velocity of the object = 8.0 m/s
∴ Ek = 1/2 × 65 kg × (8.0 m/s)² = 2,080 joules
The kinetic energy, Ek = 2,080 J
c) The total mechanical energy, Etotal = Eg + Ek
∴ Etotal = 3,060.72 j + 2,080 j = 5,140.72 J
The kinetic energy, Ek = 5,140.72 J
d) If the ramp had a total height of 8.0 m, we have;
At the 8.0 m height
Etotal = Eg(max), Ek = 0 j
With the given values, we get;
Eg(max) = 65 kg × 9.81 m/s² × 8 m = 5,101.2 joules = Etotal
Eg(max) = 5,101.2 j
Etotal = 5,101.2 j
Ek = 0 j
However, using only the values in the question with the assumption that all things being equal, we have;
Etotal = Constant = 5,140.72 j
Eg a the max height, 8.0 m = Eg(max) = Etotal = 5,140.2 j
Ek = 0 j