A 100-kg box is placed on a ramp. As one end of the ramp is raised, the box begins to move downward just as the angle of inclination reaches 15. What is the coefficient of static friction between box and ramp?

The coefficient of static friction is 0.27

Explanation:

Frictional force Ff is a force of opposition that exist between two surfaces in contact. This force opposes the moving force acting on the object. It is directly proportional to the reaction force acting on the object and this is expressed mathematically as Ff = nR where;

n is the constant of proportionality known as the coefficient of static friction.

R is the normal reaction

For a body on an inclined plane, the moving force which acts downwards and along the incline plane is equal to the frictional force acting upward the plane i.e Fm= Ff

The expression then becomes;

Fm = nR

n = Fm/R

For a body on an inclined plane;

Fm = wsin(theta) and R = wcos(theta) where;

w is the weight of the object

theta is angle of inclination = 15°

n = wsin(theta)/wcos(theta)

n = sintheta/cos(theta)

n = tan(theta)

n = tan15°

n = 0.27

The coefficient of static friction is 0.27

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when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min