Answer to Question #116092 in Mechanics | Relativity for zyn

Question

We look at a small block with a mass of 5.0 kg that is at rest in point A before it slips. The block slides along the slope plane to point B. After passing point B, it freely moves to the ground at point C. The acceleration of gravity is 9.81 m / s2. We can claim the block as a point particle in this task and we disregard air resistance.

a) Vi antar først at det ikke er friksjon mellom klossen og skr˚aplanet. Bestem klossens fart i punkt B.

Answer 1

Solution.

a)$m=5.0kg;$

$g=9.8m/s^2;$

$v_0=0;$

Since the forces of friction and resistance are absent, the unit moves under the action of gravity, the projection of which on the axis directed along the plane is equal to:

$F=mgsin\alpha$;

According to Newton's second law we have:

$ma=mgsin\alpha;\implies a=gsin\alpha;$

$S=\dfrac{v^2-v_0^2}{2a}; v_0=0 \implies v^2=2aS;$

$h$ -height of the plane, $\alpha$ - the angle of inclination of the plane;

$S=\dfrac{h}{sin\alpha};$

$v^2=2gsin\alpha\dfrac{h}{sin\alpha}=2gh;$

$v=\sqrt{2gh};$

$v=\sqrt{2\sdot9.8\sdot h}=4.43\sqrt{h} m/s;$

Answer: $v=4.43\sqrt{h} m/s;$