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balandron [24]
3 years ago
8

A bug is on the rim of a disk of diameter 9 in that moves from rest to an angular speed of 76 rev/min in 6.5 s. what is the tang

ential acceleration?
Physics
1 answer:
ehidna [41]3 years ago
5 0
Let's convert the final angular speed of the disk into rad/s:
\omega_f = 76  \frac{rev}{min} \cdot  \frac{2 \pi rad/rev}{60 s/min}=7.96 rad/s
while the initial angular speed is zero.

So, the angular acceleration of the disk is
\alpha =  \frac{\omega_f - \omega_i }{t} = \frac{7.96 rad/s}{6.5 s}=1.22 rad/s^2

The radius of the disk is half the diameter: r= d/2 = 9 m/2 =4.5 m

And so, the tangential acceleration is the angular acceleration times the radius:
a_t = \alpha r =(1.22 rad/s^2)(4.5 m)=5.49 m/s^2
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A gun shoots a bullet with a velocity of 500 m/s. The gun is aimed horizontally and fired from a height of 1.5 m. How far does t
MrMuchimi

The bullet travels a horizontal distance of 276.5 m

The bullet is shot forward with a horizontal velocity u_x. It takes a time <em>t</em> to fall a vertical distance <em>y</em> and at the same time travels a horizontal distance <em>x. </em>

The bullet's horizontal velocity remains constant since no force acts on the bullet in the horizontal direction.

The initial velocity of the bullet has no component in the vertical direction. As it falls through the vertical distance, it is accelerated due to the force of gravity.

Calculate the time taken for the bullet to fall through a vertical distance <em>y </em>using the equation,

y=u_yt+\frac{1}{2} gt^2

Substitute 0 m/s for u_y, 9.81 m/s²for <em>g</em> and 1.5 m for <em>y</em>.

y=u_yt+\frac{1}{2} gt^2\\ 1.5 m=(0m/s)t+\frac{1}{2} (9.81m/s^2)t^2\\ t=\sqrt{\frac{2(1.5m)}{9.81m/s^2} } =0.5530s

The horizontal distance traveled by the bullet is given by,

x=u_xt

Substitute 500 m/s for u_x and 0.5530s for t.

x=u_xt\\ =(500m/s)(0.5530s)\\ =276.5m

The bullet travels a distance of 276.5 m.


5 0
3 years ago
A block of mass m slides on a horizontal frictionless surface. The block is attached to a spring with a spring constant K. At th
Fittoniya [83]

Answer:

b) a = -k / m x , c) d²x / dt² = - A w² cos (wt+Ф) , d) and e)  T = 2π √m / k

h)   a = - A w² cos (wt+Ф)

Explanation:

a) see free body diagram in the attachment

b) We write Newton's second law

          Fe = m a

          -k x = ma

           a = -k / m x

c) the acceleration is

         a = d²x / dt²

     

      If x = A cos wt

        v = dx / dt = -A w sin (wt +Ф)

        a = d²x / dt² = - A w² cos (wt+Ф)

d) we substitute in Newton's second law

        d²x / dt² = -k / m x

   

We call

       w² = k / m

e) substitute to find w

     -A w² cos (wt+Ф) = -k / m A cos (wt+Ф)

      w² = k / m

Angular velocity and frequency are related

       w = 2π f

       f = 1 / T

       

 We substitute

      T = 2π / w

      T = 2π √m / k

g)    v= - A w sin (wt+Ф)

h) acceleration is

       a = - A w² cos (wt+Ф)

8 0
3 years ago
When a person steps forward out of a small boat onto a dock, the boat recoils backward in the water. why does this occur??
bixtya [17]
Here is the correct answer of the given question above. When a person steps forward out of a small boat onto a dock, the boat recoils backward in the water and this occurs because the total momentum of the system is conserved. Hope this helps.
4 0
3 years ago
Read 2 more answers
The (blank) of vibration of a wave is defined as that which has the lowest frequency
saveliy_v [14]
Fundamental frequency
6 0
3 years ago
Read 2 more answers
A car horn creates a 595 Hz tone
aliina [53]

Answer:

529 Hz

Explanation:

595(343-20)/(343 + 20) = 529

3 0
3 years ago
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