Answer to Question #100601 in Mechanics | Relativity for Aaliyah Hope

Question

A student moves a box of books down the hall
by pulling on a rope attached to the box. The
student pulls with a force of 187 N at an angle
of 20.4
◦
above the horizontal. The box has a
mass of 27.3 kg, and µk between the box and
the floor is 0.22.
The acceleration of gravity is 9.81 m/s
2
.
Find the acceleration of the box.
Answer in units of m/s
2

Answer 1

We project all the forces acting on the body on the coordinate axis

and write down the laws of motion in projection on these axes:

$N+F \cdot sin(\alpha)-m \cdot g=0$ (1)

$F \cdot cos(\alpha)-F_fr=m \cdot a$ (2)

Where

$F_fr=\mu \cdot N$ (3)

From expression (2) we express the friction force

$F_fr=F \cdot cos(\alpha)-m \cdot a$

From expression (1) we express the force N

$N=m \cdot g-F \cdot sin(\alpha)$

substitute in (3)

$F \cdot cos(\alpha)-m \cdot a=\mu\cdot (m \cdot g-F \cdot sin(\alpha))$

express acceleration

$a=\frac{F \cdot cos(\alpha)-\mu\cdot (m \cdot g-F \cdot sin(\alpha))}{m}=$

$=\frac{187 \cdot cos(20.4^0)-0.22\cdot (27.3 \cdot 9.81-187 \cdot sin(20.4^0))}{27.3}=4.787m/s^2$