Question

A box of books weighing 319 N is shoved across the floor by a force of 485 N exerted downward at an angle of 35 degrees below the horizontal.
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a. If [mu]k b/t box & floor is 0.57, how long does it take to move the box 4.00 m, starting from rest?
b. If [mu]k b/t box & floor is 0.75, how long would it take the box to move 4.00 m from rest?
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I would have gotten the answer to (a) if the acceleration was 1.7 but I somehow got around 0.17 which is off by a decimal point..
Therefore, I know that my answer to (b) will be fixed if I fix the acceleration problem with (a).

Answer 1

@Lessis ?

Answer 2

Forgot to add normal force.

Answer 3

Normal? c;
I meant I got the acceleration wrong = n =;;

Answer 4

First, for this problem, we need to calculate the normal force Fn.

Assuming my diagram is correct:

\[F_{n} = |W + F_{y}|\]
Where Fy is the force applied downwards. (You can calculate it using the sine function)

Then, you can calculate the total push force Ft:
\[F_{t} = F_{f} + F_{x}\]
Where Fx is the x componend of the applied force. (You can calculate it using the cosine function)

Then, when you have Ft, you can calculate the acceleration using F = ma.

Answer 5

.-. wat

Answer 6

These are the equations my teacher had us do in-class.
\[\Sigma F_y = N-W-F_g=\cancel{ma}^0\]\[N=W+F_g\]\[\Sigma F_x= F_x-ma\]\[a=\frac{F_x-f}{m} = \frac{Fcos \theta - \mu(w + Fsin \theta)}{m} = \frac{485cos35-0.57(319+485sin35)}{319}\]\[a \approx 1.7 m/s^2\]
However, I got a result of \[a\approx 0.17 m/s^2\]

Answer 7

Lol. I got the same answer as you, and then I noticed you divided by 319.
319 is the weight, not the mass. To get the mass, you divide the weight by g, which is 9.8 m/s^2, or just about 10.
That's where your error is from. :D

Answer 8

\[W = mg = m*9.8\frac{ m }{ s^{2} }\]
\[319 N = m * 9.8\frac{ m }{ s^{2} }\]

Answer 9

That's not my error, it'd be the teacher's error then. I realized it too, but I was confused about whether the teacher would be wrong - @Lessis

Answer 10

And that's why, if you think your result is wrong, you always have to check for the units of what you're working with. (Fx - F)/(319 N ) is a unit-less quantity.

Answer 11

Well, like I've said... it was the teacher's error, not mine .-.
I figured it would be like that. @Lessis

Answer 12

@Lessis Apparently I ended up with -1.6 m/s/s instead of -1.7 for part a). The actual number is \[-1.552137645m/s^2\]

Answer 13

The minus sign depends on how you picture the movement of the box.
Why'd you get that number? It looks kinda off. ._.

Answer 14

I have no idea lol @Lessis