A large box of mass M is moving on a horizontal floor at speed v0. A small box of mass m is sitting on top of the large box. The coefficient of static friction between the two boxes is μs and coefficient of kinetic friction between the large box and floor is μk. Find an expression for the shortest distance dmin in which the large box can stop without the small box slipping.

dmin = V0^2 / {2(9.8)(μs)}

Explanation:

According to free body diagram, the only forces acting on the small box are force of gravity and force of friction.  

Therefore, the vector sum of the forces in the horizontal direction will be,

ma = F of friction which would be ma = mgμs

a = gμs ……. (1)

Kinematics equation states that, Vf^2 = Vi^2+ 2a (delta d)

Since the large box stops moving, which means Vf = 0 and initial velocity Vi=V0, then kinematics equation becomes

0 = V0^2 + 2a (delta d)

(delta d or dmin) = V0^2/2a …… (2)

Substitute the value of a from eqn.1 in eqn. 2, we should get

dmin = V0^2 / {2(9.8)(μs)}

gans

explanation:

vestigial organs (like your appendix) are organs that no longer serve a purpose.

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.