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