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2 years ago

14

How fast do you need to swing a 250-g ball at the end of a string in a horizontal circle of 0.6-m radius so that the string make

s a 39 degree angle relative to the horizontal?

1 answer:

serious [3.7K]2 years ago

8 0

Answer:

2.7 m/s

Explanation:

Draw a free body diagram of the ball. There are two forces:

Weight force mg pulling down

Tension force T pulling 39° above the horizontal

Sum of the forces in the y direction:

∑F = ma

T sin θ − mg = 0

T = mg / sin θ

Sum of the forces in the radial (+x) direction:

∑F = ma

T cos θ = m v² / r

Substitute:

(mg / sin θ) cos θ = m v² / r

mg / tan θ = m v² / r

g / tan θ = v² / r

v = √(gr / tan θ)

Given that r = 0.6 m and θ = 39°:

v = √(9.8 m/s² × 0.6 m / tan 39°)

v ≈ 2.7 m/s

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An electron of mass 9.11 1031 kg has an initial speed of 3.00 105 m/s. It travels in a straight line, and its speed increases to

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Explanation:

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Initial speed of the electron, $u=3\times 10^5\ m/s$

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Distance, d = 5 cm = 0.05 m

(a) The acceleration of the electron is calculated using the third equation of motion as :

$a=\dfrac{v^2-u^2}{2d}$

$a=\dfrac{(7\times 10^5)^2-(3\times 10^5)^2}{2\times 0.05}$

$a=4\times 10^{12}\ m/s^2$

Force exerted on the electron is given by :

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$F=3.64\times 10^{-18}\ N$

(b) Let W is the weight of the electron. It can be calculated as :

$W=mg$

$W=9.11\times 10^{-31}\times 9.8$

$W=8.92\times 10^{-30}\ N$

Comparison,

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$\dfrac{F}{W}=4.08\times 10^{11}$

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3 years ago

A tank circuit consists of an inductor and a capacitor. Give a simple explanation for why the magnetic field in the induc- tor i

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Answer:

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A-10A twin-jet close-support airplane is approximately rectangular with a wingspan (the length perpendicular to the flow directi

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$\delta_{L} = \frac{5.2 \times 3}{\sqrt{4.1 \times 10^7}}$

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2 years ago

Give an example for each of the following, where the force:

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Explanation:

A cricket player hitting the ball from opposite direction.
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2 years ago

Read 2 more answers

. A milk truck carries milk with density 64.6 lbyft3 in a horizontal cylindrical tank with diameter 6 ft. (a) Find the force exe

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Answer:

Explanation:

one end of tank will be circular in shape . Area of circle A

= π r² , r is radius of the circle

= 3.14 x 3²

A = 28.26 ft³

To calculate force on the circular area , we first find pressure at the center of the circle which is at depth equal to r

pressure at the center = h d g ' here h = depth = r , d = density of milk

pressure = 3 x 64.6 x 32 poundal / ft²

= 6201.6 poundal / ft²

total force on circular face = pressure at the center x area of circle

= 6201.6 x 28.26

= 175257.21 poundal .

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3 years ago