Question

How much force is needed to prevent the body of a mass of 25kg from falling?

Answer 1

Answer:

12.5 kg

Explanation:

Let F force is required at any angle theta from horizontal.

Force perpendicular to horizontal plane (i.e forces in vertical plane):

Fsinθ↑mg↓

∴Normalforceontheblock,N=mg−Fsinθ↑

Force along horizontal plane:

Fcosθinthedirectionofforceapplied&frictionoppotietoit.

∴frictionforce,f=μN=μ(mg−Fsinθ)

For block to move following equation should be satisfied:

Fcosθ≥f⇒Fcosθ≥μ(mg−Fsinθ)

For least force the inequality should be equal and we will differentiate F wrt to theta to get value of theta at which force will be minimum.

F=

cosθ+μsinθ

μmg

Diff.Fw.r.ttheta

dθ

dF

=

(cosθ+μsinθ)

2

0−(−sinθ+μcosθ)

=0

tanθ=μ=

3

1

⇒cosθ=

2

3

&sinθ=

2

1

∴F=

(

3

/2)+(1/

3

)(1/2)

(1/

3

)mg

=mg/2=12.5kgf