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I am Lyosha [343]
3 years ago
14

Part A A uniform solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane. If the

angular velocity of the disk is 4.46 rad/s at the bottom, what is the height of the inclined plane?
Physics
1 answer:
kifflom [539]3 years ago
3 0

Answer:

Height will be 3.8971 m        

Explanation:

We have given that radius of the solid r = 1.60 m

Mass of the solid disk m = 2.30 kg

Angular velocity \omega =4.46rad/sec

Moment of inertia is given by I=\frac{1}{2}mr^2

Transnational Kinetic energy is given by KE=\frac{1}{2}mv^2 as we know that v = v=\omega r

So KE=\frac{1}{2}m(\omega r)^2

Rotational kinetic energy is given by KE_{ROTATIONAL}=\frac{1}{2}I\omega ^2=\frac{1}{2}\left ( \frac{1}{2}mr^2 \right )\omega ^2=\frac{1}{4}m(r\omega )^2

Potential energy is given by mgh

According to energy conservation

mgh=\frac{1}{2}m(\omega r)^2+\frac{1}{4}m(\omega r)^2

h=\frac{3r^2\omega ^2}{4g}=\frac{3\times 1.60^2\times 4.46^2}{4\times 9.8}=3.8971m

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A 40kg cart gains a KE of 200J. How fast does it go?
34kurt

Answer:

3.16 m/s

Explanation:

Use the formula

k =  \frac{m {v}^{2} }{2}  \\ v =  \sqrt{ \frac{2k}{m} }  \\ v =  \sqrt{ \frac{2(200)}{40} }  \\ v = 3.16 \frac{m}{s}

7 0
2 years ago
A student plans an investigation to determine whether an object has a positive charge, a negative charge, or is electrically neu
dangina [55]

Answer:

Hope it helps

Explanation:

The number of electrons that surround the nucleus will determine whether or not an atom is electrically charged or electrically neutral. The amount of charge on a single proton is equal to the amount of charge possessed by a single electron. A proton and an electron have an equal amount but an opposite type of charge. Thus, if an atom contains equal numbers of protons and electrons, the atom is described as being electrically neutral. On the other hand, if an atom has an unequal number of protons and electrons, then the atom is electrically charged (and in fact, is then referred to as an ion rather than an atom). Any particle, whether an atom, molecule or ion, that contains less electrons than protons is said to be positively charged. Conversely, any particle that contains more electrons than protons is said to be negatively charged

3 0
2 years ago
A hole of radius r is bored through the center of a sphere of radius r. Find the volume v of the remaining portion of the sphere
nikklg [1K]

Answer:

Πr²(4r/3 - h)

Explanation:

Volume of a sphere is 4/3Πr³. If a hole of radius r is bored through, the hole with generate a circular shape in the sphere. The volume of the remaining portion of the sphere will be the difference between the volume of the sphere and the area of the hole bored(which will be volume of a cylinder since the hole bored will create a cylindrical shape in the sphere)

Area of the remaining portion = Volume of sphere - volume of a cylinder

Volume of sphere = 4/3Πr³

Volume of a cylinder = Πr²h

Volume of the remaining portion = 4/3Πr³ - Πr²h

= Πr²(4r/3 - h)

Where h is the height of the cylindrical hole

5 0
3 years ago
Read 2 more answers
A person running has a momentum of 720 kg m/s and is traveling at a velocity of 5 m/s. What is his mass?
allsm [11]

Explanation:

Momentum is mass times velocity.

p = mv

720 kg m/s = m (5 m/s)

m = 144 kg

7 0
3 years ago
A 2000 kg car moves along a horizontal road at speed vo
cluponka [151]

Answer:

The shortest possible stopping distance of the car is 175.319 meters.

Explanation:

In this case we see that driver use the brakes to stop the car by means of kinetic friction force. Deceleration of the car is directly proportional to kinetic friction coefficient and can be determined by Second Newton's Law:

\Sigma F_{x} = -\mu_{k}\cdot N = m \cdot a (Eq. 1)

\Sigma F_{y} = N-m\cdot g = 0 (Eq. 2)

After quick handling, we get that deceleration experimented by the car is equal to:

a = -\mu_{k}\cdot g (Eq. 3)

Where:

a - Deceleration of the car, measured in meters per square second.

\mu_{k} - Kinetic coefficient of friction, dimensionless.

g - Gravitational acceleration, measured in meters per square second.

If we know that \mu_{k} = 0.0735 and g = 9.807\,\frac{m}{s^{2}}, then deceleration of the car is:

a = -(0.0735)\cdot (9.807\,\frac{m}{s^{2}} )

a = -0.721\,\frac{m}{s^{2}}

The stopping distance of the car (\Delta s), measured in meters, is determined from the following kinematic expression:

\Delta s = \frac{v^{2}-v_{o}^{2}}{2\cdot a} (Eq. 4)

Where:

v_{o} - Initial speed of the car, measured in meters per second.

v - Final speed of the car, measured in meters per second.

If we know that v_{o} = 15.9\,\frac{m}{s}, v = 0\,\frac{m}{s} and a = -0.721\,\frac{m}{s^{2}}, stopping distance of the car is:

\Delta s = \frac{\left(0\,\frac{m}{s} \right)^{2}-\left(15.9\,\frac{m}{s} \right)^{2}}{2\cdot \left(-0.721\,\frac{m}{s^{2}} \right)}

\Delta s = 175.319\,m

The shortest possible stopping distance of the car is 175.319 meters.

8 0
3 years ago
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