Aperson is pulling on a block of mass m with a force equal to its weight directed 30 above the horizontal plane across a rough surface, generating a friction 'f' on the block. if the person is now pushing downward on the block with the same force 30 degrees above the horizontal plane across the same rough surface, what is the friction on the block?

a) f

b) 1.5f

c) 2f

d) 3f

The friction on the block is 3f. Answer D.

Explanation:

Hi there!

Please, see the attached figure for a better description of the problem.

Let´s write the sum of all forces in the  vertical direction for the first case in which the person pulls on the block:

∑Fy = 0 (because the block is not accelerated in the vertical direction).

N + Fy - W = 0   (see figure, the forces in the upward direction are positive and those in the downward direction are negative)

By trigonometry: Fy = F · sin (30°) = W · sin (30°). Then:

N + W · sin (30°) - W = 0

Solving for N:

N = W (1 - sin (30°))

Then the friction force can be written as follows:

f = μ · N (where  μ is the coefficient of friction)

f =  μ · W (1 - sin (30°))  = μ· 0.5 · W

In the case in which the person is pushing, the sum of vertical forces will be expressed as follows:

N - W - Fy = 0

N - W - W · sin (30°) = 0

N = W(1 + sin (30°))

Then Fr will be:

Fr = μ · N

Fr = μ · W (1 + sin (30°))

Fr = μ · 1.5 W

Now if we divide FR / f:

Fr/f = μ · 1.5 · W /  μ· 0.5 · W

Fr/f = 3

Fr = 3f

The friction on the block is 3f. Answer D.

it has to be b, about 97 percent.

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