Question

When a 40N force, parallel to and directed up the incline, is applied to a block on a frictionless incline that is 30o above the horizontal, the acceleration of the block is 2.0 m/s2, up the incline. Find the mass of the block.

Answer 1

Answer:

5.8 kg

Explanation:

We are given that

Force,F=40 N

$\theta=30^{\circ}$

Acceleration,a=$2 m/s^2$

We have to find the mass of block.

$F_{net}=ma$

$F-mgsin\theta=ma$

$F=mgsin\theta+ma=m(gsin\theta+a)$

$40=m(9.8sin30+2)$

Where

$g=9.8m/s^2$

$40=6.9m$

$m=\frac{40}{6.9}=5.8 kg$

Answer 2

Answer:

$m=5.797\ kg$

Explanation:

GIVEN:

applied force up the inclined plane, $F=40\ N$

angle of the plank from the horizontal, $\theta=30^{\circ}$

acceleration of the body up the plane, $a=2\ m.s^{-2}$

Now from the  schematic we balance the forces:

$F-mg\sin\theta=m.a$

$F=m(g\sin\theta +a)$

$40=m(9.8\times0.5+2)$

$m=5.797\ kg$