A particle (mass m) is projected with an initial velocity v at an angle θ to the horizontal. What is the work done by the force of gravity from the instant of throwing to the instant it reaches the highest point?

Question

A particle (mass m) is projected with an initial velocity v at an angle θ to the horizontal. What is the work done by the force of gravity from the instant of throwing to the instant it reaches the highest point? (A) mv2 sin θ (B) Zero (C) -mv2 sin θ (D) (mv2 sin2 θ/2)

Tardigrade Admin · Accepted Answer

Wm g =Kf-Ki =(1/2) m(v cos θ)2-(1/2) m v2 =(1/2) m v2[ cos 2 θ-1] =-(1/2) m v2 sin 2 θ

Q. A particle (mass m) is projected with an initial velocity $v$ at an angle $θ$ to the horizontal. What is the work done by the force of gravity from the instant of throwing to the instant it reaches the highest point?

$m v^{2} sin θ$

Zero

$- m v^{2} sin θ$

$\frac{m v ^{2} s i n ^{2} θ}{2}$

$W_{m g} = K_{f} - K_{i}$
$= \frac{1}{2} m (v cos θ)^{2} - \frac{1}{2} m v^{2}$
$= \frac{1}{2} m v^{2} [cos^{2} θ - 1]$
$= - \frac{1}{2} m v^{2} sin^{2} θ$

Q. A particle (mass m) is projected with an initial velocity v at an angle θ to the horizontal. What is the work done by the force of gravity from the instant of throwing to the instant it reaches the highest point?

mv2sinθ

Zero

−mv2sinθ

2mv2sin2θ​

Wmg​=Kf​−Ki​ =21​m(vcosθ)2−21​mv2 =21​mv2[cos2θ−1] =−21​mv2sin2θ

Q. A particle (mass m) is projected with an initial velocity $v$ at an angle $θ$ to the horizontal. What is the work done by the force of gravity from the instant of throwing to the instant it reaches the highest point?

$m v^{2} sin θ$

$- m v^{2} sin θ$

$\frac{m v ^{2} s i n ^{2} θ}{2}$

$W_{m g} = K_{f} - K_{i}$
$= \frac{1}{2} m (v cos θ)^{2} - \frac{1}{2} m v^{2}$
$= \frac{1}{2} m v^{2} [cos^{2} θ - 1]$
$= - \frac{1}{2} m v^{2} sin^{2} θ$