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
zhannawk [14.2K]
3 years ago
8

A record turntable is rotating at 33 rev/min. A watermelon seed is on the turntable 4.4 cm from the axis of rotation. (a) Calcul

ate the acceleration of the seed, assuming that it does not slip. (b) What is the minimum value of the coefficient of static friction between the seed and the turntable if the seed is not to slip? (c) Suppose that the turntable achieves its angular speed by starting from rest and undergoing a constant angular acceleration for 0.37 s. Calculate the minimum coefficient of static friction required for the seed not to slip during the acceleration period.
Physics
1 answer:
romanna [79]3 years ago
5 0

Answer:

a) a =0.53 m/s²

b) μ=0.054

c) μ = 0.068

Explanation:

a) If we assume that the turntable is rotating at a constant speed, the only force acting on the seed parallel to the surface, which keeps it  from following a straight line trajectory, is the centripetal force.

So, we can apply Newton's 2nd Law to the seed in this way:

Fnet = m*a = m*ac = m*ω²*r

We have the value of the angular speed, ω, in rev/min, so it is advisable to convert it to rad/sec, as follows:

ω = 33 rev/min*(1 min/60 sec)*(2*π rad/ 1 rev) = 11/10*π rad/sec

So, replacing in (1), we can solve for ac, as follows:

ac = ω²*r = (11/10)²*π²*0.044 m = 0.53 m/s²

b) Now, the centripetal force that we found above, is not a new type of force, it must be a force that explains the behavior of the seed.

As the seed does not slip, the only force acting  on it parallel to the surface, is the static  friction force, which has a maximum value, as follows:

Ff = μ*N

As there is no movement in the vertical direction, this means that the normal force must be equal and opposite to Fg, so we can write the expression for Ff as follows:

Ff = μ*m*g

Now, this force is no other than centripetal force, so we can write this equation:

Ff  = Fc ⇒ μ*m*g = m*ac

⇒ μ*g = ac

Solving for μ:

μ = ac/g = 0.53 m/s² / 9.8 m/s² = 0.054

c) During the acceleration period, added to the centripetal acceleration, as the angular speed is not constant, we will have also an angular acceleration, γ , which we can get as follows:

γ = Δω/Δt = (11/10)*π / 0.37 s = 9.34 rad/sec²

By definition of angular acceleration, there exists a fixed  relationship between the angular acceleration and the tangential acceleration (same as the one between angular and tangential speed), as follows:

at = γ*r = 9.34 rad/sec²*0.044 m = 0.41 m/s

When the turntable has reached to its maximum angular velocity, it will have also the maximum value of the centripetal acceleration, which we have just found out.

So, the magnitude of the total acceleration (at the moment of maximum acceleration) as they are perpendicular each  other) , is given by the following expression:

a = √(ac)²+(at)² = 0.67 m/s²

Now, as friction force opposes to the relative movement between surfaces (the seed and the turntable), it shall be larger than the product of the mass times the total acceleration, acting along  the same action line, so we can say:

Ffmin = μ*m*g = m*a

⇒ μmin = a/g = 0.67 m/s²/9.8 m/s² = 0.068

You might be interested in
I need help with these. Please show workings<br>​
Sauron [17]

Answer:

Imp = 25 [kg*m/s]

v₂= 20 [m/s]

Explanation:

In order to solve these problems, we must use the principle of conservation of linear momentum or momentum.

1)

(m_{1}*v_{1})+(F*t)=(m_{1}*v_{2})

where:

m₁ = mass of the object = 5 [kg]

v₁ = initial velocity = 0 (initially at rest)

F = force = 5 [N]

t = time = 5 [s]

v₂ = velocity after the momentum [m/s]

(5*0) +(5*5) = (m_{1}*v_{2}) = Imp\\Imp = 25 [kg*m/s]

2)

(m_{1}*v_{1})+(F*t)=(m_{1}*v_{2})\\(0.075*0)+(30*0.05)=(0.075*v_{2})\\v_{2}=20 [m/s]

8 0
2 years ago
Read 2 more answers
The dimensions of a cylinder are changing, but the height is always equal to the diameter of the base of the cylinder. If the he
VashaNatasha [74]

Answer:

dV/dt  = 9 cubic inches per second

Explanation:

Let the height of the cylinder is h

Diameter of cylinder = height of the cylinder = h

Radius of cylinder, r = h/2

dh/dt = 3 inches /s

Volume of cylinder is given by

V = \pi r^{2}h

put r = h/2 so,

V = \pi \frac{h^{3}}{4}

Differentiate both sides with respect to t.

\frac{dV}{dt}=\frac{3h^{2}}{4}\times \frac{dh}{dt}

Substitute the values, h = 2 inches, dh/dt = 3 inches / s

\frac{dV}{dt}=\frac{3\times 2\times 2}{4}\times 3

dV/dt  = 9 cubic inches per second

Thus, the volume of cylinder increases by the rate of 9 cubic inches per second.

6 0
3 years ago
Help ASAP <br><br>Identify the cause of foliation in rocks?
rewona [7]
When minerals are exposed to high pressure and temperatures, the individual minerals begin to realign themselves
5 0
3 years ago
Se colocan tres objetos, muy cerca uno del otro, dos al mismo tiempo. Cuando se juntan los objetos A y B, se repelen. Cuando se
docker41 [41]

Answer:

Los objetos A y C tienen cargas del mismo signo (opcion a)

Explanation:

Hay dos tipos de cargas : cargas positivas y cargas negativas.

La Ley de Coulomb dice que la fuerza electrostática entre dos cargas puntuales es proporcional al producto de las cargas e inversamente proporcional al cuadrado de la distancia que las separa, y tiene la dirección de la línea que las une y se cumple que:

  • La fuerza ejercida sobre una carga apunta hacia la otra cuando las dos tienen distinto signo (fuerza atractiva).
  • El sentido de la fuerza se dirige hacia el lado opuesto de la carga cuando ambas tienen el mismo signo (fuerza repulsiva).

Es decir que las cargas de igual signo se repelen, mientras que las de diferente signo se atraen.

Entonces, si se juntan los objetos A y B y se repelen significa que la carga es del mismo signo.

Cuando se acercan los objetos B y C, se repelen. Entonces significa que posee carga de igual signo.

Por lo que podes concluir que <u><em>los objetos A y C tienen cargas del mismo signo (opcion a)</em></u>

8 0
2 years ago
A biker first accelerates from 0.0 m/s to 6.0 m/s in 6 s, then continues at this speed for 5 s. What is the total distance trave
Svetradugi [14.3K]

Answer:

48m

Explanation:

Given the following data;

Initial velocity = 0m/s

Final velocity = 6m/s

Time, t = 6 secs

Time, T2 = 5 secs

Mathematically, acceleration is given by the equation;

Acceleration (a) = \frac{final \; velocity  -  initial \; velocity}{time}

Substituting into the equation;

a = \frac{6 - 0}{6}

a = \frac{6}{6}

Acceleration, a = 1m/s²

<u>To find the distance covered in the first phase;</u>

<em>Solving for distance, we would use the second equation of motion;</em>

S = ut + \frac {1}{2}at^{2}

<em>Substituting the values into the equation;</em>

S = 0(6) + \frac {1}{2}*1*(6)^{2}

S = 0 + \frac {1}{2}*1*36

S = 0.5 *36

Distance, S1 = 18m

<u>For the second phase, time T2 = 5 secs;</u>

<em>Mathematically, speed is given by the equation;</em>

Speed = \frac{distance}{time}

<em>Making distance the subject of formula, we have;</em>

Distance, S = speed * time

<em>Substituting into the above equation;</em>

Distance, S = 6 * 5

Distance, S2 = 30m

Total distance = S1 + S2 = 18m + 30m = 48m

Total distance = 48m

<em>Therefore, the total distance traveled by the biker is 48m.</em>

4 0
3 years ago
Other questions:
  • The process by wich metamorphic rock changes to igneous rock begins with
    10·1 answer
  • A mass hanging from a vertical spring is in simple harmonic motion as given by the following position function, where t is measu
    7·1 answer
  • Which universal force acts on protons and neutrons in an atom's nucleus?
    5·2 answers
  • Now, consider whether the following statements are true or false:_____________________________________.
    14·1 answer
  • You are riding in an elevator that is accelerating upward. Suppose you stand on a scale. The reading on the scale is __________.
    13·2 answers
  • A water wheel rotates with a period of 2.26 s. If the water wheel has a radius of l.94 m,
    7·1 answer
  • What studies the natural world around us
    14·2 answers
  • A metre rule is used to measure a length Which reading is shown to the nearest millimetre? A 0.7 m B 0.76 m с 0.761 m D 0.7614 m
    9·1 answer
  • While working out, a man performed 500 J of work in 8 seconds. What washis power?A. 4000 WB. 62.5 WC. 500 WD. 38.5 W
    12·1 answer
  • how fast would a(n) 73 kgkg man need to run in order to have the same kinetic energy as an 8.0 gg bullet fired at 430 m/sm/s ?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!