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
Ksivusya [100]
3 years ago
12

A 4-lb ball b is traveling around in a circle of radius r1 = 3 ft with a speed (vb)1 = 6 ft>s. if the attached cord is pulled

down through the hole with a constant speed vr = 2 ft>s, determine the ball's speed at the instant r2 = 2 ft. how much work has to be done to pull down the cord? neglect friction and the size of the ball

Physics
1 answer:
Leya [2.2K]3 years ago
6 0
Position #1:
radius, r₁ = 3 ft
Tangential speed, v₁ = 6 ft/s

By definition, the angular speed is
ω₁ = v₁/r₁ = (3 ft/s) / (3 ft) = 1 rad/s

Position #2:
Radius, r₂ = 2 ft

By definition, the moment of inertia in positions 1 and 2 are respectively
I₁ = (4 lb)*(3 ft)² = 36 lb-ft²
I₂ = (4 lb)*(2 ft)² = 16 lb-ft²

Because momentum is conserved,
I₁ω₁ = I₂ω₂
Therefore the angular velocity in position 2 is
ω₂ = (I₁/I₂)ω₁
      = (36/16)*1 = 2.25 rad/s
The tangential velocity in position 2 is
v₂ = r₂ω₂ = (2 ft)*(225 rad/s) = 4.5 ft/s

At each position, there is an outward centripetal force.
In position 1, the centripetal force is
F₁ = m*(v²/r₂) = (4)*(6²/3) = 48 lbf
In position 2, the centripetal force is
F₂ = (4)*(4.5²/2) = 40.5 lbf

The radius diminishes at a rate of 2 ft/s.
Therefore the force versus distance curve is as shown below.

The work done is the area under the curve, and it is
W = (1/2)*(48.0+40.5 ft)*(3-2 ft) = 44.25 ft-lb

Answer:  44.25 ft-lb


You might be interested in
Need help with number <br> 50 <br> PLEASE HELP! Show all work please!
Pavel [41]

Answer:50 is b

Explanation:

v = 34757

6 0
3 years ago
A series RLC circuit with L = 12 mH, C = 3.5 mu or micro FF, and R = 3.3 ohm is driven by a generator with a maximum emf of 115
Elan Coil [88]

Explanation:

Given data

Inductance L=12*10^-³H

Capacitance C= 3.5*10^-6F

Resistance R= 3.3 Ohms

Voltage V=115v

Capacitive reactance Xc=?

inductive reactance Xl=?

Impedance Z=?

Phase angle =?

A. Resonance frequency

In RLC circuit resonance occurs when capacitive reactance equals inductive reactance

f=1/2pi √ LC

f=1/2*3.142 √ 12*10^-³*3.5*10^-6

f=1/6.284*0.0002

f=1/0.00125

f=800HZ

B. Find Irms at resonance.

Irms=R/V

Irms=3.3/115

Irms=0.028amp

Find the capacitive reactance XC in Ohms

Xc=1/2pi*f*C

Xc=1/2*3.142*800*3.5*10^-6

Xc=1/0.0176

Xc=56.8 ohms

To find the inductive reactance

Xl=2pifL

Xl=2*3.142*800*12*10^-3

Xl=60.3ohms

d) Find the impedance Z.

Z=√R²+(Xl-Xc)²

Z=√3.3²+(60.3-56.8)²

Z=√10.89+12.25

Z=√23.14

Z=4.8ohms

Phase angle =

Tan phi=Xc/R=56.8/3.3

Tan phi=17.2

Phi=tan-1 17.2

Phi= 1.51°

6 0
3 years ago
Assume that a magnetic field exists and its direction is known. Then assume that a charged particle moves in a specific directio
katen-ka-za [31]
 The first right-hand rule determines the directions of magnetic force, conventional current and the magnetic field.  Given any two of theses, the third can be found. 
The second Right-Hand Rule determines the direction of the magnetic field around a current-carrying wire and vice-versa<span> </span>
So, assuming that a magnetic field <span>exists and its direction is known and assuming that a charged particle moves in a specific direction through that field with velocity (v(, to determine the direction of force on the particle we should use the second right-hand rule.</span>
4 0
3 years ago
Three-dimensional ____ programs allow designers to rotate designs of 3-d objects to view them from any angle.
notsponge [240]
Long phrase is the blank
5 0
3 years ago
A 4.0 kg ball is traveling at 3.0 m/s and strikes a wall. The ball bounces off the wall with a velocity of 4.0 m/s in the opposi
trasher [3.6K]

Answer:

280 N

Explanation:

Applying Newton's third second law of motion,

F = m(v-u)/t................... Equation 1

Where F = Magnitude of the average force on the ball during contact, v = final velocity of the ball, u = initial velocity of the ball, t = time of contact of the ball and the wall.

Note: Let the direction of the initial velocity of the ball be positive

Given: m = 4 kg, u = 3.0 m/s, v = -4.0 m/s (bounce off), t = 0.1 s

Substitute into equation 1

F = 4(-4-3)/0.1

F = 4(-7)/0.1

F = -28/0.1

F = -280 N.

Note: The negative sign tells that the force on the ball act in opposite direction to the initial motion of the ball

3 0
3 years ago
Other questions:
  • Jennifer has taught her pet rat to run a maze. She thinks that the rat will
    15·1 answer
  • What accurately describes the relationship between brain damage and language impairment?
    15·2 answers
  • A sample has a mass of 15 g and a volume of 3mL
    11·1 answer
  • What is the sequence of energy transformations associated with a hydroelectric dam?
    13·2 answers
  • The atoms in a sample of carbon must contain nuclei with the same number of
    14·1 answer
  • Force
    13·1 answer
  • Never start a job without knowing the _______and_______ of the chemicals you are working with a) properties and hazards b) SDS a
    8·1 answer
  • What is the average temperature of the city, 89.6 Fahrenheit, on the Celsius scale?
    7·1 answer
  • What does sound need to travel?​
    12·2 answers
  • [2.21] Please help me find a) and b)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!