Mathematics: Sam applies a force at 30° to the horizontal to move a football tackling dummy 10 m horizontally. He does 160 J of mechanical work. Determine the magnitude of the force by using vector dot product.

Sam applies a force at 30° to the horizontal to

Ответ:

adam4119

22.06.2021

Mathematics

$F=\frac{32\sqrt{3}}{3}\text{\:or\:} \approx 18.48\:\text{N}$

Step-by-step explanation:

We can find the horizontal component of force he applied by using the formula for work:

$W=F\Delta x$

Solving for force, we have:

$160=F\cdot 10,\\F=16\:\text{N}$

However he applied the original force at an angle of $30^{\circ}$ to the horizontal. This force of 16 newtons is only the horizontal component of that force. To find the magnitude of the original force, we can use basic trigonometry:

$\cos 30^{\circ}=\frac{16}{x},\\x=\frac{16}{\cos 30^{\circ}},\\\\x=\frac{16}{\frac{\sqrt{3}}{2}},\\\\x=16\cdot\frac{2}{\sqrt{3}}=\frac{32}{\sqrt{3}}=\boxed{\frac{32\sqrt{3}}{3}}$

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Sam applies a force at 30° to the horizontal to move a football tackling dummy 10 m horizontally. He does 160 J of mechanical work. Determine the magnitude of the force by using vector dot product.

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