Ablock of mass m=16.8 kg is sliding on a surface with initial velocity v=23.2 m/s. the block has a coefficient of kinetic friction μk =0.426 with respect to the surface and is being pushed by a force of magnitude f=86.4 n in the direction of its motion. due to kinetic friction, the block is slowing down. how long will it take for the block to come to a stop?

t = 23.92 s

Explanation:

Newton's second law:

∑F = m*a Formula (1)

∑F : algebraic sum of the forces in Newton (N)

m : mass s (kg)

a : acceleration  (m/s²)

We define the x-axis in the direction parallel to the movement of the block  and the y-axis in the direction perpendicular to it.

Forces acting on the block

W: Weight of the block : In vertical direction, downward

FN : Normal force : perpendicular to the floor, upward

fk :  Kinetic friction force: parallel to the floor  and opposite to the movement

F = 86.4 N , in the direction of the motion

Calculated of the W

W= m*g

W=  16.8 kg* 9.8 m/s² = 164.64 N

Calculated of the FN  

We apply the formula (1)  

∑Fy = m*ay ay = 0  

FN - W = 0  

FN = W  

FN =  164.64 N

Calculated of the fk

fk  = μk*FN

fk  = 0.426* 164.64 N

fk  = 70.13 N

We apply the formula (1) to calculated acceleration of the block:

∑Fx = m*ax  ,  ax= a  : acceleration of the block

F - fk = m*a

86.4 -70.13  = (16.8)*(-a)

16.26 =  (16.8)*(-a)

a = -(16.26 )/ (16.8)

a = - 0.97 m/s²

Kinematics of the block

Because the block moves with uniformly accelerated movement we apply the following formula :

vf = v₀ + a*t   Formula (2)

Where:  

t: time interval  (m)

v₀: initial speed  (m/s)

vf: final speed   (m/s)

Data:

v₀ = 23.2 m/s

vf = 0

a =  -0.97 m/s²  

Time it takes for the block to stop

We replace data in the formula (2)  to calculate the time

vf= v₀+a*t

0 = 23.2+( -0.97)*t

(0.97)*t  = 23.2

(0.97)*t  = 23.2

t = 23.2 / (0.97)

t = 23.92 s

0.11 m/s and 0.28 m/s should be correct

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.