Question

A body, when acted upon by a force of 10 kgf, gets displaced by 0.5 m. Calculate the work done by the force, when the displacement is

(i) in the direction of force,

(ii) at an angle of 60o with the force, and

(iii) normal to the force. (g= 10Nkg-1)

​

Answer 1

Explanation:

↪Force acting on the body = 10 kgf

↪10 × 10 N

↪ 100 N

↪ Displacement, S = 0.5 m

(i) In the direction of force,

↪W = F × S

↪ W = 100 × 0.5

↪W = 50 J

(ii) At an angle of 60° with the force,

↪W = F × S cos θ

↪W = 100 × 0.5 cos 60°

↪W = 100 × 0.5 × 0.5 [cos 60° = 0.5]

↪W = 25 J

(iii) Normal to the force.

↪Work = force × displacement in the direction of force

↪W = F × S cos θ

↪W = 100 × 0.5 cos 90°

↪W = 100 × 0.5 × 0 [cos 90° = 0]

↪W = 0

Answer 2

Given :

• Force acting = 10kgf (g = 10Nkg⁻¹)
• Displacement = 0.5 m

To find :

• Work done ; in the direction of force
• Work done ; at an angle of 60° with the force
• Work done with normal to the force

Solution :

Here, force acting = 10kgf

                              = (10 × g)

                              = (10kg × 10Nkg⁻¹) N

                              = 100 N

(i) Work done in the direction of force is given by,

$: \implies\underline{\boxed{\sf{Work \ done = Force \times Displacement }}} \\\\ \\ : \implies\sf Work \ done = (100 \times 0.5) \ J \\\\ \\ : \implies\underline{\boxed{\sf{Work \ done = 50 \ J }}} \ \bigstar$

$\rule{280}{1}$

(ii) Work done at an angle of 60° with the force,

$: \implies\underline{\boxed{\sf{Work \ done = F\times s \times cos\theta }}} \\\\ \\ : \implies\sf Work \ done = 100 \times 0.5 \times cos60^{\circ} \\\\ \\ : \implies\sf Work \ done = 100 \times 0.5 \times 0.5 \qquad[\because cos60^{\circ} = 0.5] \\\\ \\ : \implies\underline{\boxed{\sf{Work \ done = 25 \ J }}} \ \bigstar$

$\rule{280}{1}$

(iii) Work done with normal to the force :

$: \implies\underline{\boxed{\sf{Work \ done = F \times s \times cos90^{\circ} }}} \\\\ \\ : \implies\sf Work \ done = 100 \times 0.5 \times 0 \qquad[\because cos90^{\circ} = 0] \\\\ \\ : \implies\underline{\boxed{\sf{Work \ done = 0 }}} \ \bigstar$