How did you manage to overcome the difficulties that arose?

9. A 5.0 kg block on an inclined plane is acted upon by a horizontal force of 100 N shown in the figure below. The coefficient o

Helga [31]

Answer:

A: The acceleration is 7.7 m/s up the inclined plane.

B: It will take the block 0.36 seconds to move 0.5 meters up along the inclined plane

Explanation:

Let us work with variables and set

$m=5kg\\\\F_H=100N\\\\\mu=0.3\\\\\theta=37^o.$

As shown in the attached free body diagram, we choose our coordinates such that the x-axis is parallel to the inclined plane and the y-axis is perpendicular. We do this because it greatly simplifies our calculations.

Part A:

From the free body diagram we see that the total force along the x-axis is:

$F_{tot}=mg*sin(\theta)+F_s-F_Hcos(\theta).$

Now the force of friction is $F_s=\mu*N,$ where $N$ is the normal force and from the diagram it is $F_y=mg*cos(\theta).$

Thus $F_s=\mu*N=\mu*mg*cos(\theta).$

Therefore,

$F_{tot}=mg*sin(\theta)+\mu*mg*cos(\theta)-F_Hcos(\theta)\\\\=mg(sin(\theta)+\mu*cos(\theta))-F_Hcos(\theta).$

Substituting the value for $F_H,m,\mu, and \:\theta$ we get:

$F_{tot}= -38.63N.$

Now acceleration is simply

$a=\frac{F_H}{m} =\frac{-38.63N}{5kg} =-7.7m/s.$

The negative sign indicates that the acceleration is directed up the incline.

Part B:

$d=\frac{1}{2} at^2$

Which can be rearranged to solve for t:

$t=\sqrt{\frac{2d}{a} }$

Substitute the value of $d=0.50m$ and $a=7.7m/s$ and we get:

$t=0.36s.$

which is our answer.

Notice that in using the formula to calculate time we used the positive value of $a$ , because for this formula absolute value is needed.

5 0

4 years ago

You need to design a banked curve at the new circular Super 100 Raceway. The radius of the track is 800 m and cars typically tra

uysha [10]

Answer:

$33.1^{\circ}$

Explanation:

Let's start by writing the equations of the forces along the two directions:

- Vertical:

$N cos \theta = mg$

where

N is the normal reaction

$\theta$ is the angle between the road and the horizontal

(mg) is the weight of the car, with m being its mass and g the acceleration of gravity

- Horizontal:

$N sin\theta = m \frac{v^2}{r}$

where

v is the speed of the car

r is the radius of the turn

Dividing the 2nd equation by the 1st one, we get:

$tan \theta = \frac{v^2}{rg}$

In this problem:

$r = 800 m$ (radius of the turn)

$v=160 mi/h = 71.5 m/s$ is the speed

$g=9.8 m/s^2$

Substituting, we find:

$\theta= tan^{-1} (\frac{v^2}{rg})=tan^{-1}(\frac{(71.5)^2}{(800)(9.8)})=33.1^{\circ}$

8 0

4 years ago

A static charge is different from an electric current, in that a static charge __

Vesna [10]

Static charge occurs when there is an imbalance of positively and negatively charged atoms, so this one should be the last option that it involves ions as well.

Hope this helps :)

5 0

4 years ago

A race car travels on a circular track at an average rate of 125 mi/h. The radius of the track is 0.320 miles. What is the centr

GREYUIT [131]

The centripetal acceleration of the car is 48,800 mi/h2

4 0

4 years ago

Where is information first stored in a human brain

Dmitrij [34]

Answer:

The long-term memories are stored throughout the brain as groups of neurons, the brain stores memories in three ways--Short-term memories, Sensory memory and Long-term memory the human brain cell can hold 5 times as much of information as the Encyclopedia Britannica.

Explanation:

I hope this helps, I got this from a website called Stack Exchange :)

7 0

3 years ago

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