Answer to Question #212674 in Physics for Josh

Question

A block of mass 5 kg starts to slide down a frictionless plane, inclined at 25° as shown in figure 2. The block moves from rest at the top. The length of the incline is 2.0m. Find (a) the acceleration of the block, and (b) its speed when it reaches the bottom of the inclined.

Answer 1

Given:

$\theta=25^{\circ}$

$l=2.0\:\rm m$

$g=9.8\:\rm m/s^2$

(a) The Newton's second law gives

$$ma=F=mg\sin\theta$$ $$a=g\sin\theta=\rm 9.8\: m/s^2*\sin 25^{\circ}=4.1\: m/s^2$$

(b) The law of conservation of energy gives

$$mgh=\frac{mv^2}{2}$$ $$v=\sqrt{2gh}=\sqrt{2gl\sin\theta}\\ =\sqrt{2*9.8*2.0*\sin 25^{\circ}}=4.1\:\rm m/s$$