A6.0-kg box slides down an inclined plane that makes an angle of 39o with the horizontal. if the coefficient of kinetic friction is 0.40, at what rate does the box accelerate down the slope? 3.1m/s23.4m/s23.7m/s24.1m/s2

A. 3.1m/s²

Explanation:

Since the body is sliding down the plane, the frictional force (Ff) being a force of opposition will be acting upwards.

The forces acting on the body in the vertical direction will be the weight (W) and the normal reaction(R) acting in the opposite direction.

Taking the sum of the forces along the plane,

Fm - Ff = mass × acceleration (newton's law)

Since Fm = Wsin(theta)

Ff = nR where n is the coefficient of friction we will have;

Wsin(theta) - nR = ma... (1)

W = mg = 6×10 = 60N

n = 0.40

R = Wcos (theta) {resolving weight to the vertical)

R = 60cos39°

R = 46.6N

Substituting this values into eqn 1 to the get the acceleration,

60sin39° - 0.4(46.6) = 6a

37.8 - 18.64 = 6a

19.16 = 6a

a = 19.16/6

a = 3.19m/s²

The acceleration of the body down the plane will be 3.1m/s²

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.