Answer:
a = 3.52 m/s²
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)
Data
m= 27.4 kg : mas of the box
F= 170 N, at an angle of 25◦ above the horizontal :Force rope attached to the box
μk = 0.293 :Coefficient of friction between box and floor
g = 9.8 m/s² : acceleration due to gravity
We define the x-axis in the direction parallel to the movement of the box and the y-axis in the direction perpendicular to it.
Forces acting on the box
W: Weight of the block : In vertical direction ,downward
FN : Normal force : perpendicular to the floor upward
f : Friction force: parallel to the floor and opposite to the movement
F : force of the rope attached to the box , at an angle of 25◦ above the horizontal
Calculated of the W ( weight of the box)
W= m*g
W= 27.4 kg* 9.8 m/s² = 268.52 N
x-y components of the force of 170 N
Fx=170 N *cos 25° = 154.07 N
Fy=170 N *sin 25° =71.845 N
Calculated of the FN ( Normal force)
We apply the formula (1)
∑Fy = m*ay ay = 0
FN + Fy - W = 0
FN = W- Fy
FN = 268.52 N - 71.845 N
FN =196. 675 N
Calculated of the f (friction force)
f = μk*FN
f = 0.293*196. 675
f = 57.626 N
We apply the formula (1) to calculated acceleration of the box:
∑Fx = m*ax , ax= a : acceleration of the box
Fx-f = m*a
154.07-57.626 = (27.4)*a
96.45 = (27.4)*a
a = (96.45)/ (27.4)
a = 3.52 m/s²
