An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable breaks when the elevator is at a height h above the top of the spring, calculate the value that the spring constant k should have so that passengers undergo an acceleration of no more than 7.0 g when brought to rest. Let M be the total mass of the elevator and passengers. Express your answer in terms of the variables h, M, and appropriate constants.
k = ?

Explanation:

Acceleration will be in upward direction due to force by spring in upward direction .Let maximum compression be x .

maximum force  = k x -Mg

k x - Mg = 7Mg

kx = 8Mg

After falling by height h , compression in spring is x

1/2 k x² = Mg( h + x )

1/2 x 8Mg x = Mgh +Mgx

4Mgx = Mgh +Mgx

3 Mgx = Mgh

x = h / 3

kx = 8Mg

k h/3 = 8Mg

k = 24 Mg / h

to treat tumors in the body

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.