- #1

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*A projectile is launched from ground level at a 45 degree angle. How much work does gravity do on the projectile between its launch and when it hits the ground?*

Gravity will do as much work on the object as the work performed by the

y-component of the force that launched the projectile.

[tex]

W_{gravity} =\Delta K_{gravity}

\]

\[

\Delta K_{gravity} =\frac{1}{2}mv_y^2

\]

\[

\Delta K_{gravity} =\frac{1}{2}m\left( {\sin (45)v} \right)^2

\]

\[

W_{gravity} =\frac{1}{2}m\left( {\sin (45)v} \right)^2

[/tex]

*A hockey player pushes a puck of mass 0.50 kg across the ice using a constant force of 10.0 N over a distance of 0.50 m. How much work does the hockey player do? If the puck was initially stationary, what is its final speed? (Ignore friction.)*

[tex]W=Fd, W=10N*0.5m, W=5N[/tex]

[tex]

F=ma

\quad

\Rightarrow

\quad

a=\frac{F}{m}

\]

\[

a=\frac{10.0N}{0.50kg}

\quad

\Rightarrow

\quad

a=\frac{10.0\rlap{--} {k}\rlap{--} {g}\cdot m/s^2}{0.50\rlap{--}

{k}\rlap{--} {g}}

\]

\[

a=20m/s^2

\]

\[

v_f^2 =v_i^2 +2a\Delta d

\quad

\Rightarrow

\quad

v=\sqrt {v_i^2 +2a\Delta d}

\]

\[

v=\sqrt {\left( {2\cdot 20\frac{m}{s^2}} \right)\cdot 0.50m}

\]

\[

v=4.5m/s

[/tex]

*If a constant force F=(30.N)i, + (50.N)j acts on a particle that undergoes a displacement (4.0m)i + (1.0m)j , how much work is done on the particle?*

[tex]

W=Fd

\]

\[

W=\sqrt {\left( {3.0N} \right)^2+\left( {5.0N} \right)^2} \cdot \sqrt

{\left( {4.0m} \right)^2+\left( {1.0m} \right)^2}

\]

\[

W=20J

[/tex]