Respuesta :
Answer:
Her final velocity at she moves over the the bottom of the ramp is approximately 1.20204 m/s
Explanation:
The data of the energy used by the person in the wheel chair are;
The work done by the person, W = 70.8 J
The initial position of the wheel chair = At the bottom of the ramp
The time the person takes to do the work, t = 1.00 s
The number of turns she turned the wheel chair = 1/4 turns
The radius of the wheel of the wheel chair, r = 40 cm
The mass of her and the wheel chair, m = 98.0 kg
By the conservation of energy principle, we have;
The total mechanical energy of the motion, M.E. = The amount of work done by her in moving up the ramp = 70.8 J
M.E. = P.E. + K.E. = Constant
Where;
P.E. = Potential energy
K.E. = Kinetic energy
At the height she reached the ramp, M.E. = P.E. = 70.8 J
At the bottom of the ramp, P.E. = 0 J, therefore;
K.E. = 70.8 J
We have;
K.E. = (1/2)·m·v²
Where;
m = The mass of her and the wheelchair = 98.0 Kg
v = Her final velocity at the bottom of the ramp
By substitution, we have;
70.8 J = (1/2) × 98.0 Kg × v²
v² = 70.8/((1/2) × 98.0) = 354/245
v = √(1,770)/35 ≈ 1.20204
Her final velocity as she passed back over the bottom of the ramp, v ≈ 1.20204 m/s.
