While sliding a couch across a floor, Andrea and Jennifer exert forces FA and F on the couch. Andrea's force is due north with a
magnitude of 140.0 N and Jennifer's force is 260 east of north with a magnitude of 220.0 N (a) Find the net force (in N) in component form. net : (b) Find the magnitude (in N) and direction (in degrees counterclockwise from the east axis) of the net force magnitude direction X o counterclockwise from the east axis (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force Fos (in N) should they push so that the couch does not move? (Express your answer in vector form.) Fos
1 answer:
Answer:
See the answers and the explanation below.
Explanation:
To solve this problem we must make a free body diagram with the forces applied as well as the direction. In the attached images we can see the nomenclature of the direction of the forces and the free body diagram.
a)
<u>Sum of forces in y-axis</u>
<u />
Fy = 140 - (220*sin(10))
Fy = 101.8 [N]
<u>Sum of forces in x-axis</u>
<u />
Fx = - (220*cos(10))
Fx = - 216.65 [N]
b)
For the above result, for there to be balance we realize that we need one equal to the resulting y-axis but in the opposite direction and another opposite force in direction but equal in magnitude on the x-axis.
Fy = - 101.8 [N]
Fx = 216.65 [N]
c )
Now we need to use the Pythagorean theorem to find the result of these forces.
And the direction will be as follows.
α = tan^(-1) (101.8 / 216.65)
α = 25.16° (south to the east)
F = 216.65 i - 101.8 j [N]
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Answer:
Weight=686.7N, , S.G.=0.933, F=17.5N
Explanation:
So, the first value the problem is asking us for is the weight of methanol. (This is supposing there is a mass of methanol of 70kg inside the tank). We can find this by using the formula:
W=mg
so we can substitute the data the problem provided us with to get:
which yields:
W=686.7N
Next, we need to find the density of methanol, which can be found by using the following formula:
we know the volume of methanol is 75L, so we can convert that to like this:
so we can now use the density formula to find our the methanol's density, so we get:
Next, we can us these values to find the specific gravity of methanol by using the formula:
when substituting the known values we get:
so:
S.G.=0.933
We can now find the force it takes to accelerate this tank linearly at
F=ma
F=17.5N