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A body of mass of 4kg is on the point of slipping down the plane inclined at 30°. what force parallel to the plane will just move it up the plane?

User Sonhu
by
7.2k points

1 Answer

7 votes

Answer:To solve this problem, we can use the concept of forces and motion along an inclined plane. The forces involved are the gravitational force acting vertically downward and the force parallel to the plane.

Let's denote the following:

m = mass of the body = 4 kg

g = acceleration due to gravity =

9.8

/

2

9.8 m/s

2

θ = angle of inclination = 30°

N = normal force (perpendicular to the plane)

f = force parallel to the plane

The gravitational force acting parallel to the inclined plane is given by

sin

(

)

mgsin(θ), and the normal force is given by

=

cos

(

)

N=mgcos(θ).

When the body is on the point of slipping up the plane, the force

f just balances the component of the gravitational force acting parallel to the plane.

The component of the gravitational force parallel to the plane is

sin

(

)

mgsin(θ).

So, the equation for equilibrium is:

=

sin

(

)

f=mgsin(θ)

Now, substitute the known values:

=

(

4

)

×

(

9.8

/

2

)

×

sin

(

3

0

)

f=(4 kg)×(9.8 m/s

2

)×sin(30

)

=

4

×

9.8

×

0.5

f=4×9.8×0.5

=

19.6

f=19.6 N

Therefore, the force parallel to the plane that will just move the body up the plane is

19.6

19.6 N.

Step-by-step explanation:

User Jeffrey Sun
by
7.8k points