A confused dragonfly flies forward and backward in a straight line. Its motion is shown on the following graph of horizontal pos
ition xxx vs. time ttt.
1 answer:
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Answer:
The acceleration of the crate is 1.8 m/s² so the answer is a.
Explanation:
The very first thing you must do when solving this problem is to draw a free body diagram. (The body diagram is attached to this answer)
So once we got the free body diagram, we can analyze it and build our sum of forces in the x and y directions. Notice that according to the diagram, there are 4 forces to this problem, Normal (N), Weight (W), kinetic friction (fk) and the 750N force.
As one may see in the free body diagram, two of the forces are vertical forces: N and W, so we can use them to build a sum of forces:
Starting with the sum of forces in the y-direction, we get:
Σ=0
We set the sum equal to zero because there is no movement in the y-direction, so the system is in vertical equilibrium.
so the sum will be:
when solving for N we get that:
N=W
where W is found by multiplying the mass of the crate by the acceleration of gravity:
N=250kg*9.8m/s²
N=2450N
Once we found the normal force, we can use it to find the kinetic friction which is given by the following formula:
μ
where μ is the kinetic friction coefficient.
So we get that the kinetic friction is:
so
With this information we can go ahead and find the sum of horizontal forces:
Σ=ma
In this case the sum is equal to mass times acceleration because the crate is moving horizontally due to the action of a force, so it will have an acceleration.
so the sum of forces look like this:
750N-=ma
so
750N-294N=(250kg)a
when solving for a we get:
so the crate's acceleration is 1.82m/s².
The equilibrium condition allows finding the result for the tension of the cable that supports the block is:
- The tension is: T₁ = 270.66 N
Newton's second law gives a relationship between force, mass and the acceleration of bodies, when the acceleration is zero it is called the equilibrium condition.
A free-body diagram of the forces is shown in the attachment.
Let's write the equilibrium equation for the vertical axis.
2 - f - W = 0
2 = W + f
Let's use trigonometry to find the tension, as the angle indicates that it is relative to the vertical.
cos 30 =
= T1 cos 30
We substitute.
2T₁ cos 30 = W + f
T₁ = m g + f / 2 cos 30
T₁ =
T₁ = 270.66 N
In conclusion using the equilibrium condition we can find the result for the tension of the cable that supports en bloc is:
- The tension is: 270.66 N
Learn more here: brainly.com/question/14725331
