1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ugo [173]
3 years ago
7

A bar on a hinge starts from rest and rotates with an angular acceleration α = 12 + 5t, where α is in rad/s2 and t is in seconds

. Determine the angle in radians through which the bar turns in the first 4.88 s.
Physics
1 answer:
Rama09 [41]3 years ago
5 0

Answer:

Ф = 239.73 rad

Explanation:

α = 12 + 15×t

W = ∫α×dt

   = ∫(12 + 5×t)×dt

   = 12×t + 2.5×t^2

then:

Ф = ∫W×dt

   = ∫(12×t + 2.5×t^2)dt

   = 6×t^2 + 5/6×t^3

therefore the angle at t = 4.88s is:

Ф = 6×(4.88)^2 + 5/6×(4.88)^3

   = 239.73 rad    

You might be interested in
A student (m = 68 kg) falls freely from rest and strikes the ground. During the collision with the ground, he comes to rest in a
Gnesinka [82]

Answer:

5.7141 m

Explanation:

Here the potential and kinetic energy will balance each other

mgh=\frac{1}{2}mv^2\\\Rightarrow v=\sqrt{2gh}

This is the initial velocity of the system and the final velocity is 0

t = Time taken = 0.04 seconds

F = Force = 18000 N

a = Acceleration

g = Acceleration due to gravity = 9.81 m/s²

Equation of motion

v=u+at\\\Rightarrow a=\frac{v-u}{t}

From Newton's second law

F=ma\\\Rightarrow F=m\frac{v-u}{t}\\\Rightarrow 18000=68\frac{0-\sqrt{2gh}}{0.04}\\\Rightarrow \frac{18000}{68}\times 0.04=-\sqrt{2\times 9.81\times h}\\\Rightarrow 10.58823=-\sqrt{2\times 9.81\times h}

Squarring both sides

112.11061=2\times 9.81\times h\\\Rightarrow h=\frac{112.11061}{2\times 9.81}\\\Rightarrow h=5.7141\ m

The height from which the student fell is 5.7141 m

5 0
3 years ago
To visit your favorite ice cream shop, you must travel 490 m west on Main Street and then 920 m south on Division Street. Suppos
topjm [15]

Answer:

a) The magnitude of your average velocity during the 121 s is 8.61 m/s.

b) The direction of the average velocity is 61.9° south of west.

c) Your average speed during the trip is 11.7 m/s

Explanation:

Hi there!

a) The average velocity (a.v) is calculated as the displacement divided by the time it took to do such a displacement.

The displacement is calculated as the distance between the initial position and the final position:

Displacement = Δ(x,y) = final position - initial position

Let's consider that your initial position is the origin of our frame of reference and let's also consider that west and south are positive directions (+x and +y respectively). Then the displacement vector will be:

Δ(x,y) = final positon - initial position

Δ(x,y) = (490, 920) m - (0, 0) m = (490, 920) m

The average velocity will be:

a.v = Δ(x,y) / t

a.v = (490, 920) m / 121 s

a.v = (4.05, 7.60) m/s

The magnitude of the average velocity is calculated as follows:

 

The magnitude of your average velocity during the 121 s is 8.61 m/s.

b) To find the direction of the average velocity, we have to use trigonometric rules of right triangles. Notice that the x and y-components of the average velocity (vx and vy) together with the average velocity vector (v), with magnitude 8.61 m/s, form a triangle (see figure).

Also, notice that v is the hypotenuse of the triangle and that vx is the side adjacent to the angle θ while vy is the side opposite to θ.

Using trigonometry, we can calculate the value of the angle θ:

cos θ = adjacent side / hypotenuse

cos θ = vx / v

cos θ = 4.05 m/s / 8.61 m/s

θ = 61.9°

The direction of the average velocity is 61.9° south of west.

c) The average speed (a.s) is calculated as the traveled distance (d) divided by the time it took to cover that distance (t). In total, you traveled (490 m + 920 m) 1410 m in 121 s, then the average speed will be:

a.s = d/t

a.s = 1410 m / 121 s

a.s = 11.7 m/s

Your average speed during the trip is 11.7 m/s

5 0
3 years ago
Examine the cross-sectional slice of a stem of a mint plant. Which statement most specifically describes mint?
Maslowich

The available options are:

Mint is a dicot.

Mint is a monocot.

Mint is an angiosperm.

Mint is a bulb plant.

Answer:

Mint is a dicot.

Explanation:

Given the fact that Mint is considered to be a member of Lamiaceae, an angiosperm plant which is characterized by typically having leaves that consist of reticulate vacation and appears like veins in structure. It also has a seed that contains two cotyledons.

Hence, it is considered a DICOT PLANT due to these characteristics. The botanical name of Mint is referred to as Mentha arvensis.

7 0
2 years ago
Which of the given will facilitate a normal Diels–Alder reaction?
babymother [125]

Answer:

D

Explanation:

-  The rate of the Diels-Alder is orders of magnitude faster if there is an electron-withdrawing group on the dienophile. For example, replacing a hydrogen on ethene with the electron-withdrawing group CN results in about a 10^5 increase in the reaction rate.

- Other common electron withdrawing functional groups that will accelerate the Diels Alder reaction of dienophiles include aldehydes, ketones, and esters.

- In short, any functional group conjugated with the pi bond which can act as a pi acceptor will accelerate a Diels-Alder reaction with a typical diene.

- See attachment for graphical explanation.

7 0
3 years ago
When the units are smaller,<br> we need (more / less) of them.
lbvjy [14]

Answer:

more..................

6 0
3 years ago
Read 2 more answers
Other questions:
  • Direction of current in a solenoid depends on the direction of magnetic field
    6·1 answer
  • What is the correct name for this formula: SiO2?
    14·2 answers
  • A block of mass 10 kg slides down an inclined plane that has an angle of 30. If the inclined plane has no friction and the block
    7·2 answers
  • _____ are formed where bumps from two surfaces come into contact ?
    15·1 answer
  • Which expression should appear in the blue box to compute percent error? Accepted value – Experimental value Accepted value × Ex
    6·1 answer
  • A car initially traveling at 32.4 m/s undergoes a constant negative acceleration of magnitude 1.70 m/s2 after its brakes are app
    11·1 answer
  • hydroelectric energy is based on the blank energy of water being converted to blank energy as waterfalls and pushes against the
    12·2 answers
  • 2.List two changes an unbalanced force can cause.
    5·1 answer
  • Pls help quick too.................
    15·1 answer
  • The occupants of a vehicle not wearing a seat belt, traveling at a speed of 50 mph and colliding head-on with another vehicle, w
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!