Tilt the surface, load the block, pull on it at an angle and change the grip. Every arrow is drawn to its true size on one shared scale, so their lengths can be compared directly. Watch what the normal force does as the slope steepens — it does not follow the weight.
Normal force N = mg cosθ − F sinφ
98.98 N
The surface pushes back with 84 per cent of the weight.
Friction f
24.74 N
Kinetic friction, mu-k times N, acting up the slope.
Acceleration a = ΣFx / m
4.9153 m/s²
Net force along the surface58.98 N
0.501 g, pointing down the slope.
Weight resolved on the tilted axes
Weight117.72 N
Down the slope40.26 N
Into the surface110.62 N
Only the part into the surface has to be balanced by N.
Status
Sliding and speeding up
Static friction ran out, so the block breaks away.
Mass m12.0 kg
Surface angle θ20°
Applied force F45 N
Pull angle φ15°
Static friction μs0.25
Kinetic friction μk0.25
Gravity is fixed at g = 9.81 m/s² — it is not a control here. Angles are set in degrees and converted to radians internally. The block starts at rest, the applied force acts down the surface, and the pull angle φ is measured up from the surface itself, not from the horizontal.
Try this: set the applied force to zero, then walk the angle up one degree at a time. The block holds, holds, holds — then breaks away the moment tanθ passes μs.