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Anna [14]
3 years ago
14

You wish to buy a motor that will be used to lift a30-kg bundle of shingles from the ground to the roof of a house. The shingles

are to have a1.5-m/s2 upward acceleration at the start of the lift. The very light pulley on the motor has a radius of 0.13m . Determine the minimum torque that the motor must be able to provide.
Physics
1 answer:
hodyreva [135]3 years ago
6 0

Answer:

the minimum value of torque is 101.7 N-m.

Explanation:

Given that,

Mass of bundle of shingles, m = 30 kg

Upward acceleration of the shingles,

The radius of the motor of the pulley, r = 0.3 m

Let T is the tension acting on the shingles when it is lifted up. It can be calculated as :

T-mg=ma

T=m(g+a)

T=10\times (9.8+1.5)\\T = 113 N

Let \tau is the minimum torque that the motor must be able to provide. It is given by :

\tau=r\times T\tau=0.3\times 339\tau=101.7\ N-m

the minimum value of torque is 101.7 N-m.

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Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let |a| = 22 lb and |b| = 16 lb. Rou
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Incomplete question as the angle between the force is not given I assumed angle of 55°.The complete question is here

Two forces, a vertical force of 22 lb and another of 16 lb, act on the same object. The angle between these forces is 55°. Find the magnitude and direction angle from the positive x-axis of the resultant force that acts on the object. (Round to one decimal places.)  

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Explanation:

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Solution

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Total Force

F=F_{1}+F_{2}\\ F_{2}=22j+13.12i+9.176j\\F_{2}=13.12i+31.176j

The Resultant Force is given as

|F|=\sqrt{x^{2} +y^{2} }\\|F|=\sqrt{(13.12)^{2} +(31.176)^{2} }\\ |F|=33.8lb

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We can find the angle bu using tanα=y/x

So

tan\alpha =\frac{31.176}{13.12}\\ \alpha =tan^{-1} (\frac{31.176}{13.12})\\\alpha =67.2^{o}

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