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2 years ago

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A 20.00 kg lead sphere is hanging from a hook by a thin, massless wire 2.80 m long and is free to swing in a complete circle. Tr

eat the sphere as a point mass. Suddenly it is struck horizontally by a 5.00 kg steel dart that embeds itself in the lead sphere. What must be the minimum initial speed of the dart so that the combination makes a complete circular loop after the collision

1 answer:

Tema [17]2 years ago

3 0

The minimum initial speed of the dart so that the combination makes a complete circular loop after the collision is 58.5 m/s.

<h3>Minimum speed for the object not fall out of the circle</h3>

The minimum speed if given by tension in the wire;

T + mg = ma

T + mg = m(v²)/R

tension must be zero for the object not fall

0 + mg = mv²/R

v = √(Rg)

<h3>Final speed of the two mass after collision</h3>

Use the principle of conservation of energy

K.Ef = K.Ei + P.E

¹/₂mvf² = ¹/₂mv² + mg(2R)

¹/₂vf² = ¹/₂v² + g(2R)

¹/₂vf² = ¹/₂(Rg) + g(2R)

vf² = Rg + 4Rg

vf² = 5Rg

vf = √(5Rg)

vf = √(5 x 2.8 x 9.8)

vf = 11.7 m/s

<h3>Initial speed of the dart</h3>

Apply principle of conservation of linear momentum for inelastic collision;

5v = vf(20 + 5)

5v = 11.7(25)

5v = 292.5

v = 58.5 m/s

Learn more about linear momentum here: brainly.com/question/7538238

#SPJ1

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3 years ago

A sled drops 50 meters in height on a hill. The mass of the rider and sled is 70 kg and the sled is going 10 m/s at the bottom o

navik [9.2K]

Answer:

Efficiency = 10.2 %

Explanation:

Given the following data;

Mass = 70 kg

Height = 50 m

Velocity = 10 m/s

We know that acceleration due to gravity is equal to 9.8 m/s².

To find the efficiency of energy conversion from potential to kinetic;

First of all, we would determine the potential energy;

P.E = mgh

P.E = 70 * 9.8 * 50

P.E = 34300 J

For the kinetic energy;

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K.E = ½ * 70 * 10²

K.E = 35 * 100

K.E = 3500

Therefore, Input energy, I = 34300 J

Output energy, O = 3500 J

Next, we find the efficiency;

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Substituting into the formula, we have;

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4 0

3 years ago

Junior slides across home plate during a baseball game. If he has a mass of 115 kg, and the coefficient of kinetic friction betw

tatyana61 [14]

Weight Force of Junior = m g = 115kg x 9.81 m/s^2 = 1128.15N then compute for the friction force

Friction Force= WF x (coefficient of kinetic friction) = 1128.15N x 0.35 = 394.8525N or 395N

But you can compute in a straightway:

Solution:

= 115 x 9.81 x 0.35

= 394.85

= 395 N

It will still give the same results.

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3 years ago

Read 2 more answers

A 50-loop circular coil has a radius of 3 cm. It is oriented so that the field lines of a magnetic field are perpendicular to th

nikitadnepr [17]

Answer:

-17.8 V

Explanation:

The induced emf in a coil is given as:

$E = \frac{-NdB\pi r^2}{dt}$

where N = number of loops

dB = change in magnetic field

r = radius of coil

dt = elapsed time

From the question:

N = 50

dB = final magnetic field - initial magnetic field

dB = 0.35 - 0.10 = 0.25 T

r = 3 cm

dt = 2 ms = 0.002 secs

Therefore, the induced emf is:

$E = \frac{-50 * 0.25 * \pi * 0.03^2}{0.002} \\E = -17.8 V$

Note: The negative sign implies that the EMf acts in an opposite direction to the change in magnetic flux.

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3 years ago

A ball falls from the top of a building. As it falls, its speed increases. Which type of energy is the ball gaining as it falls?

Elina [12.6K]

<h2>Hello!</h2>

The answer is: B. Kinetic energy

<h2>Why?</h2>

Since the ball is falling, speed increases because the gravity acceleration is acting. When speed increases, the kinetic energy increases too, so the ball is gaining kinetic energy.

The gravity acceleration is equal to $9.81\frac{m}{s^{2}}$ , it means that when falling, the ball will increase it's speed 9.81m every second.

We can calculate the kinetic energy by using the following formula:

$KE=\frac{1}{2}*m*v^{2}$

Where:

$m=mass\\v=velocity$

Have a nice day!

<h2 />

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4 years ago