Question

koi hai ?
A 80 N crate Slides with the constant speed a distance of 5m downward along a rough slope that makes an angle of 30° with the horizontal The work done by the force of gravity is?​

Answer 1

Given:

• Weight of the crate is W = 80 N
• Downward distance travelled by the crate along the slope is d = 5m
• Angle of the slope is $\theta$ = 30$\degree$

To Find:

• The work done by the force of gravity = ?

Solution:

The expression of the work done by the gravitational force on the crate along the slope is

${\qquad}{\star{\underline{\boxed{\sf{\pmb{w = fg sin \theta}}}}}} \\ \\ {\qquad}{\star{\underline{\boxed{\sf{\pmb{w = w sin\theta d}}}}}}$

where,

• W is the work done
• F_g is the gravitational force

According to the question —

$\sf \implies \: w =80 sin30 \degree \times 5 \\ \\ \sf \implies \: w = 40 \times 5 \\ \\ \sf \implies \: w = 200 \: joule$

Hence,the work done by force of gravity is 200 J.

Answer 2

$\underline{ \underline{ \Large \mathfrak{Information \: given \: to \: us:-}}}$

• 80 N crate Slides with the constant speed a distance of 5m downward
• Angle created is of 30⁰.

$\underline{ \underline{ \Large \mathfrak{What \: we \: have \: to \: calculate:-}}}$

• Total work done

$\underline{ \underline{ \Large \mathfrak{Required \: formulas \: to \: solve\: this \: question:-}}}$

• $\dag \: \underline{ \boxed{ \sf{ \: W \: = \: F \: \times \: S \:cos \theta}}}$

$\red \bigstar \: \underline{\sf{It \: states \: that:-}}$

• W = Force × component of displacement in direction of force

$\underline{ \underline{ \Large \mathfrak{Performing \: the \: calculations:-}}}$

$\red \bigstar \: \underline{\sf{We \: also \: know \: that:-}}$

• $\boxed{\sf{sin30 {}^{0} \: = \: \dfrac{1}{2} }}$

$\red \bigstar \: \underline{\sf{Again \: we \: have:-}}$

• W = 80N
• D = 5m

$\red \bigstar \: \underline{\sf{Evaluating \: the \: values:-}}$

• $: \longrightarrow \: \sf{ W \: = \: 80 \: \times \: 5 \: \times \: \dfrac{1}{2} }$

$\red \bigstar \: \underline{\sf{Solving \: it \: now:-}}$

• $: \longrightarrow \: \sf{ W \: = \: \cancel{80} \: \times \: 5 \: \times \: \dfrac{1}{ \cancel2} }$

• $: \longrightarrow \: \sf{ W \: = \: 40\: \times \: 5 \: \times \: 1 }$

• $: \longrightarrow \: \sf{ W \: = \: 200 \: \times \: 1 }$

• $: \longrightarrow \: \boxed{ \bf{ W \: = \: 200} }$

Always remember that work done is measured in Joules.

$\red \bigstar \: \underline{\sf{Therefore, \: work \: done \: is \: 200J }}$

$\underline{ \underline{ \Large \mathfrak{Important \: things \: to \: remember:-}}}$

• The amount of work done by a force is equal to the product of force and displacement
• When a force acts on a body and body doesn't moves it means that displacement is zero.
• Amount of work done depends on two factors magnitude of force and displacement created by force.
• Work is said to be done only when the amount of force which is applied to the body makes it move.

The amount of work done depends on two factors:

• Magnitude of force applied
• Displacement produced by the force.