Answered

A box that has a mass of 80 kg slides down a ramp with a 30 degree angle. The free-body diagram shows the forces acting on the box. Ignoring friction and air resistance, what is the acceleration of the box, to the nearest tenth?

-0.5 m/s2

-4.9 m/s2

-8.5 m/s2

-9.8 m/s2

Verified Answer :

acceleration=4.9m/s^2

skyluke89

The force responsible for sliding the block down along the ramp is the component of the weight parallel to the ramp.

The weight of the block is

\(W=mg=(80 kg)(9.8 m/s^2)=784 N\)

The component of the weight parallel to the ramp is

\(W_{par} = W sin 30^{\circ}= (784 N)( sin 30^{\circ} )=392 N\)

And now we can find the acceleration of the box by using Newton's second law:

\(a=\frac{F}{m}=\frac{392 N}{80 kg}=4.9 m/s^2\)


So, the correct answer is

-4.9 m/s2

(the negative just means we have taken "upward along the ramp" as positive direction)

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