If one mile is 5280 feet, how many inches are in 3.94 km?

A record turntable is rotating at 33 rev/min. A watermelon seed is on the turntable 2.3 cm from the axis of rotation. (a) Calcul

VLD [36.1K]

Answer:

a) $a_{r} = 0.275\,\frac{m}{s^{2}}$ , b) $\mu_{s} = 0.028$ , c) $\mu_{s} = 0.036$

Explanation:

a) The linear acceleration of the watermelon seed is:

$a_{r} = \omega^{2}\cdot r$

$a_{r} = \left[\left(33\,\frac{rev}{min} \right)\cdot \left(2\pi\,\frac{rad}{rev} \right)\cdot \left(\frac{1}{60}\,\frac{min}{s} \right)\right]^{2}\cdot (0.023\,m)$

$a_{r} = 0.275\,\frac{m}{s^{2}}$

b) The watermelon seed is experimenting a centrifugal acceleration. The coefficient of static friction between the seed and the turntable is calculated by the Newton's Laws:

$\Sigma F = \mu_{s}\cdot m\cdot g = m\cdot a$

$a = \mu_{s}\cdot g$

$\mu_{s} = \frac{a}{g}$

$\mu_{s} = \frac{0.275\,\frac{m}{s^{2}} }{9.807\,\frac{m}{s^{2}} }$

$\mu_{s} = 0.028$

c) Angular acceleration experimented by the turntable is:

$\alpha = \frac{\omega-\omega_{o}}{\Delta t}$

$\alpha = \frac{3.456\,\frac{rad}{s}-0\,\frac{rad}{s} }{0.36\,s}$

$\alpha = 9.6\,\frac{rad}{s^{2}}$

The tangential acceleration experimented by the watermelon seed is:

$a_{t} = \left(9.6\,\frac{rad}{s^{2}} \right)\cdot (0.023\,m)$

$a_{t} = 0.221\,\frac{m}{s^{2}}$

The linear acceleration experimented by the watermelon seed is:

$a = \sqrt{a_{t}^{2}+a_{r}^{2}}$

$a = \sqrt{\left(0.221\,\frac{m}{s^{2}} \right)^{2}+\left(0.275\,\frac{m}{s^{2}} \right)^{2}}$

$a = 0.353\,\frac{m}{s^{2}}$

The minimum coefficient of static friction is:

$\mu_{s} = \frac{0.353\,\frac{m}{s^{2}} }{9.807\,\frac{m}{s^{2}} }$

$\mu_{s} = 0.036$

4 0

3 years ago

A cat accelerates from rest to 10m/s when it sees a dog. This takes 2 seconds. What was the acceleration of the cat

Nookie1986 [14]

The formula is a= chance in velocity/time
A=10-0/2
A=10/2
A=5 m/s^2 (meters per second squared)

5 0

3 years ago

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What is the velocity of an object that has a momentum of 4,000 kg-m/s and a mass of 115 kg? Round to the nearest hundredth.

iren [92.7K]

Answer:

B. 34.78 m/s

Explanation:

Momentum of a body or an object is given as the product of its velocity and its mass.

Therefore;

Momentum= velocity x mass

But; velocity = ? mass =115 kg , momentum = 4,000 kgm/s

Thus; velocity= momentum/mass

= 4,000/115

= 34.78 m/s

6 0

3 years ago

Why are recessive traits not seen even though they are present in the alleles?

Rama09 [41]

Answer:

Explanation:. The vending machine holds 10 bags of pretzels and 8 packs of cheese crackers. Both the pretzels and crackers dispenseat 2 bags per hour. How many hours will elapse when there is the same number of snacks remaining in the vending machine? How many of each item will there be at this point?Equation1______________________________Equation2_______________________________Hours: ___________________________ Items: ____________________________What does each equation have n common? ______________________How does this affect the solution?

3 0

3 years ago

A cheetah can run at 105 feet per second, but only for 7 seconds, at which time the animal must stop and rest. A fully rested ch

shepuryov [24]

Answer:

5 seconds

Explanation:

The straight line distance between (0, 0) and the antelope's position (x, y) at time t can be found using distance formula:

d² = x² + y²

d² = (-39 + 40t)² + (228 + 30t)²

d² = 1521 - 3120t + 1600t² + 51984 + 13680t + 900t²

d² = 53505 + 10560t + 2500t²

The cheetah can run a total distance of:

105 * 7 = 735

The time t at this distance is:

735² = 53505 + 10560t + 2500t²

540225 = 53505 + 10560t + 2500t²

0 = -486720 + 10560t + 2500t²

0 = -24336 + 528t + 125t²

t = 12, -16.224

t can't be negative, so t = 12.

Therefore, the cheetah can wait 5 seconds before it has to start running.

5 0

3 years ago

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