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

`m=5.797\ kg`

Step-by-step 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*0.5+2)`

`m=5.797\ kg`

Answer 2

5.8 kg

Step-by-step 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=(40)/(6.9)=5.8 kg`