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
bazaltina [42]
3 years ago
9

The wheel and the attached reel have a combined weight of 50lb and a radius of gyration about their center of 6 A k in = . If pu

lley B that is attached to the motor is subjected to a torque of M ft lb = − 50 , determine the velocity of the 200lb crate after the pulley has turned 5 revolutions. Neglect the mass of the pulley

Engineering
1 answer:
marishachu [46]3 years ago
3 0

The complete question is;

The wheel and the attached reel have a combined weight of 50 lb and a radius of gyration about their center of ka = 6 in. If pulley B that is attached to the motor is subjected to a torque of M = 50 lb.ft, determine the velocity of the 200lb crate after the pulley has turned 5 revolutions. Neglect the mass of the pulley.

The image of this system is attached.

Answer:

Velocity = 11.8 ft/s

Explanation:

Since the wheel at A rotates about a fixed axis, then;

v_c = ω•r_c

r_c is 4.5 in. Let's convert it to ft.

So, r_c = 4.5/12 ft = 0.375 ft

Thus;

v_c = 0.375ω

Now the mass moment of inertia about of wheel A about it's mass centre is given as;

I_a = m•(k_a)²

The mass in in lb, so let's convert to slug. So, m = 50/32.2 slug = 1.5528 slug

Also, let's convert ka from inches to ft.

So, ka = 6/12 = 0.5

So,I_a = 1.5528 × 0.5²

I_a = 0.388 slug.ft²

The kinetic energy of the system would be;

T = Ta + Tc

Where; Ta = ½•I_a•ω²

And Tc = ½•m_c•(v_c)²

So, T = ½•I_a•ω² + ½•m_c•(v_c)²

Now, m_c is given as 200 lb.

Converting to slug, we have;

m_c = (200/32.2) slugs

Plugging in the relevant values, we have;

T = (½•0.388•ω²) + (½•(200/32.2)•(0.375ω)²)

This now gives;

T = 0.6307 ω²

The system is initially at rest at T1 = 0.

Resolving forces at A, we have; Ax, Ay and Wa. These 3 forces do no work.

Whereas at B, M does positive work and at C, W_c does negative work.

When pulley B rotates, it has an angle of; θ_b = 5 revs × 2π rad/revs = 10π

While the wheel rotates through an angle of;θ_a = (rb/ra) • θ_b

Where, rb = 3 in = 3/12 ft = 0.25 ft

ra = 7.5 in = 7.5/12 ft = 0.625 ft

So, θ_a = (0.25/0.625) × 10π

θ_a = 4π

Thus, we can say that the crate will have am upward displacement through a distance;

s_c = r_c × θ_a = 0.375 × 4π

s_c = 1.5π ft

So, the work done by M is;

U_m = M × θ_b

U_m = 50lb × 10π

U_m = 500π

Also,the work done by W_c is;

U_Wc = -W_c × s_c = -200lb × 1.5π

U_Wc = -300π

From principle of work and energy;

T1 + (U_m + U_Wc) = T

Since T1 is zero as stated earlier,

Thus ;

0 + 500π - 300π = 0.6307 ω²

0.6307ω² = 200π

ω² = 200π/0.6307

ω² = 996.224

ω = √996.224

ω = 31.56 rad/s

We earlier derived that;v_c = 0.375ω

Thus; v_c = 0.375 × 31.56

v_c = 11.8 ft/s

You might be interested in
If you’re still enrolled in school, but are looking for a job, on your resume you should highlight:
Ann [662]

Answer:

c

Explanation:

7 0
3 years ago
Jen is developing the positioning statement for a new line of sunglasses. In a meeting, the marketing team tells Jen that she ha
Allushta [10]

Answer:

Unique Selling Proposition

Explanation:

Unique Selling Proposition (USP) is the distinguishing feature that makes one product or business better than its competitor in the market. Jen has developed a competitive advantage of the new sunglasses brand making the company to sell their products. This is an example of USP.

8 0
3 years ago
A PMOS device with VT P = −1.2 V has a drain current iD = 0.5 mA when vSG = 3 V and vSD = 5 V. Calculate the drain current when:
Ksju [112]
The answer is b ! Hope I helped
7 0
2 years ago
Suppose a student rubs a Teflon rod with wool and then briefly touches it to an initially neutral aluminum rod suspended by insu
Oliga [24]

Answer:

Due to touch of teflon, its charge will reduce but will not go to zero. Some amount of its initial charge will be transferred to Aluminum rod. So, aluminum rod will have a non-zero negative charge.

Explanation:

3 0
3 years ago
(Blank) welding involves manual welding with equipment anomalously controls one or more of the windy conditions while (blank) we
shepuryov [24]

Answer:

D.

Explanation:

In automated welding, defined as “welding with equipment that requires only occasional or no observation of the weld, and no manual adjustment of the equipment controls,” the welder's involvement is limited to activating the machine to initiate the welding cycle and observing the weld on an intermittent basis.

8 0
3 years ago
Other questions:
  • Consider a cubical furnace with a side length of 3 m. The top surface is maintained at 700 K. The base surface has emissivity of
    13·1 answer
  • The value of the critical Reynolds number for the flow over a flat plate is 5 x10^5. The significance of the value is:
    13·1 answer
  • What's the best way to find the load capacity of a crane? Select the best option. Call the manufacturer Ask co-workers Look at t
    8·1 answer
  • The pressure intensity at a point in a fluid is equal in all directions a.true b.false​
    12·1 answer
  • Which happens when a wave passes through an opening
    12·2 answers
  • What forced induction device is more efficient?
    8·2 answers
  • When mass is the same, what is the relationship between radius and compression strength?
    5·1 answer
  • 10 properties of metals?<br> ​
    10·2 answers
  • What is the density of the mass of 24.0g and a volume of 6 ml?
    13·1 answer
  • Derive the expression ε=ln(1+e), where ε is the true strain and e is the engineering strain. Note that this expression is not va
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!