Susan's 13.0 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30∘ above the floor. The tension is a constant 29.0 N and the coefficient of friction is 0.170.

Question: Use work and energy to find Paul's speed after being pulled 2.60 m.

Paul's speed is 2.93m/s.

Explanation:

Let's call the tension on the rope and Paul's mass.  

The normal force on Paul equals his weight minus the upward vertical pull from the rope :

since

Therefore, the frictional force is

.

Thus, the net horizontal force on Paul is

where is the horizontal component of rope's tension and it is

therefore, the net force becomes

Now, when this horizontal net force pulls Paul by a horizontal distance , the work done is

and according to the work-kinetic energy theorem

which gives

solving for we get:

Finally, we put in numerical values

,

,

,

to get

Hence, when Paul is pulled by 2.60m, his speed becomes 2.93m/s.

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.

0.55x745.7j and a calculator