Question

In all of the following answers, enter formulas using the following symbols: m for mass, g for gravitational acceleration. theta (enter as theta) for the angle of the inclined plane, mu (enter as mu) for the coefficient of friction, the functions sin and cos. and simple numbers like 0 as needed. What is the weight of the object on the ramp? w = What is the magnitude of the component of the weight normal to the ramp? w = What is the acceleration of the object normal to the ramp? a = What is the sum of forces normal to the ramp? sigma F = What is the magnitude of the normal force? N = What is the magnitude of the component of the weight parallel TO the ramp? w_|| = What is the magnitude of the frictional force on the object sliding down the ramp? f What is the sum of forces parallel to the ramp? sigma F_|| =

Answer 1

Part A) w = mg

Part B) $w_{\perp }= mg\cos \theta$

Part C) $ma_{\perp }= N-mg\cos \theta = 0\Rightarrow a_{\perp } = 0$

Part D) $\sum F_{\perp }= N-mg\cos \theta = 0$

Part E) $N=mg\cos \theta$

Part F) $w_{//}=mg \sin \theta$

Part G) $f = \mu N = \mu mg\cos \theta$

Part H) $\sum F_{//} =mg\sin \theta -f$

$\sum F_{//} =mg\sin \theta -\mu mg\cos \theta$

$\sum F_{//} =m(g\sin \theta -\mu g\cos \theta)$