12. A person in a wheelchair did 70.8 J of work on the chair to get it moving from rest at the bottom of a ramp, taking 1.00 s to do so. She turned the wheel (which has a radius of 40.0 cm) one quarter turn before letting go and rolling back down. If the combined mass of her and the chair was 98.0 kg, what was her final velocity when she passed back over the bottom of the ramp?

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WILL GIVE

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.

i'm thinking more like energy

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.