AP Physics 1

Object Pulled an Incline With Friction

A Block of Mass 3.0 kg is being pulled up a ramp by a rope that is parallel to the ramp surface, which is inclined at 25 degrees from the horizontal. The block accelerates at 1 $\frac{m}{s^2}$ up the ramp, and the coefficient of kinetic friction between the block and the surface is 0.20. Determine the tension in the rope.



Typed Out Solution

Given Weight Calculation
$Mass = 3kg$
$a = 1 \frac{m}{s^{2}}$
$F_g = mg$
$F_g = 3(9.81)$
$F_g = 29.43 N$
Components of the Weight Sum of the Forces in the X Direction Sum of the Forces in the Y Direction
$F_{gx} = F_gsin\left (\theta \right )$
$F_{gx} = 29.43sin(25^{\circ} )$
$F_{gx} = 12.44 N$

$F_{gy} = F_gcos(\theta )$
$F_{gy} = 29.43cos(25^{\circ} )$
$F_{gy} = 26.67 N$
Find Sum of the forces in the x Direction:
$\sum F_x =F_T-F_{gx} -F_r =ma$
$F_T-12.44 -0.2F_N =(3)(1)$
$F_T=12.44 +0.2F_N +(3)(1)$
$F_T=12.44 +0.2(26.67) +(3)(1)$
$F_T = 20.77 N$
Find Sum of the forces in the x Direction:
There is no vertical acceleration
$\sum F_y =F_N-F_{gy} =0$
$F_N =F_{gy}$
$F_N = 26.67 N$
Substitute into $F_N$ that
appears in the x direction
forces