Question

A man pushes on a piano with mass 190 kgkg ; it slides at constant velocity down a ramp that is inclined at 18.0 ∘∘ above the horizontal floor. Neglect any friction acting on the piano.Calculate the magnitude of the force applied by the man if he pushes

(a) parallel to the incline and
(b) parallel to the floor.

Answer 1

The magnitude of applied force,parallel to the incline is 575.38 N and parallel to the floor is 605 N.

Step-by-step explanation:

Given:

Mass of the piano
`(m)` = 190 kg

Inclined angle
`(\theta)` = 18 degree

Considering gravity,
`g` = 9.8
`ms^-^2`

And

Using,
`sin(18) =0.30` and
`cos(18)=0.95`

FBD diagram is attached with all the force acting on the floor and and the inclined.

We have to find the magnitude of forces,when the man pushes it parallel to the incline and to the floor.

a.

When the man pushes it parallel to the incline.

Balancing the forces as
`\sum F=0` .

⇒
`F+mgsin(\theta) =0`

⇒
`F=-mgsin(\theta)`

⇒ Here it is negative as the force is acting downward.

⇒ Plugging the values of mass
`(m)` and angle
`(\theta)` .

⇒
`F=190* 9.8* sin(18)`

⇒
`F=575.38` N

b.

When the force is parallel to the floor.

⇒
`Fcos(\theta)=mgsin(\theta)`

⇒
`F=(mgsin(\theta))/(cos(\theta))`

⇒ Plugging the values.

⇒
`F=(190* 9.8* sin(18))/(cos(18))`

⇒
`F=605` N

So,

The magnitude of applied force in inclined direction is 575.38 Newton and parallel to the floor is 605 N.