A uniformly dense solid disk with a mass of 4 kg and a radius of 4 m is free to rotate around an axis that passes through the center of the disk and perpendicular to the plane of the disk. The rotational kinetic energy of the disk is increasing at 21 J/s. If the disk starts from rest through what angular displacement (in rad) will it have rotated after 3.3 s?

Answers

Answer 1

Answer:

Answer:

3.44 rad

Explanation:

The rotational kinetic energy change of the disk is given by ΔK = 1/2I(ω² - ω₀²) where I = rotational inertia of solid sphere = MR²/2 where m = mass of solid disk = 4 kg and R = radius of solid disk = 4 m, ω₀ = initial angular speed of disk = 0 rad/s (since it starts from rest) and ω = final angular speed of disk

Since the kinetic energy is increasing at a rate of 21 J/s, the increase in kinetic energy in 3.3 s is ΔK = 21 J/s × 3.3 s = 69.3 J

So, ΔK = 1/2I(ω² - ω₀²)

Since ω₀ = 0 rad/s

ΔK = 1/2I(ω² - 0)

ΔK = 1/2Iω²

ΔK = 1/2(MR²/2)ω²

ΔK = MR²ω²/4

ω² = (4ΔK/MR²)

ω = √(4ΔK/MR²)

ω = 2√(ΔK/MR²)

Substituting the values of the variables into the equation, we have

ω = 2√(ΔK/MR²)

ω = 2√(69.3 J/( 4 kg × (4 m)²))

ω = 2√(69.3 J/[ 4 kg × 16 m²])

ω = 2√(69.3 J/64 kgm²)

ω = 2√(1.083 J/kgm²)

ω = 2 × 1.041 rad/s

ω = 2.082 rad/s

The angular displacement θ is gotten from

θ = ω₀t + 1/2αt² where ω₀ = initial angular speed = 0 rad/s (since it starts from rest), t = time of rotation = 3.3 s and α = angular acceleration = (ω - ω₀)/t = (2.082 rad/s - 0 rad/s)/3.3 s = 2.082 rad/s ÷ 3.3 s = 0.631 rad/s²

Substituting the values of the variables into the equation, we have

θ = ω₀t + 1/2αt²

θ = 0 rad/s × 3.3 s + 1/2 × 0.631 rad/s² (3.3 s)²

θ = 0 rad + 1/2 × 0.631 rad/s² × 10.89 s²

θ = 1/2 × 6.87159 rad

θ = 3.436 rad

θ ≅ 3.44 rad

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A particle moves through an xyz coordinate system while a force acts on it. When the particle has the position vector r with arrow = (2.00 m)i hat − (3.00 m)j + (2.00 m)k, the force is F with arrow = Fxi hat + (7.00 N)j − (5.80 N)k and the corresponding torque about the origin is vector tau = (3.40 N · m)i hat + (2.80 N · m)j + (0.800 N · m)k. Determine Fx.

Answers

Answer:

-4.40

Explanation:

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A bicycle consists of which types of simple machines? Check all that apply. lever

Answers

Answer:

Lever, pulley and wheel and axle are the types of machine it's grouped to

Explanation:

The wheel and axle is a simple machine that works by reducing friction in trying to move a load. This is seen in the Tyre of the bicycle

Pulley is a simple machine that creates a mechanical advantage and supports the changing of direction for a rope or cable. This is seen in the chain of the bicycle

Levers attached to the bike's pedals are pushed down to direct force into the pulley system.

A bike is compound machine.This means that it is made up of a bunch of different simple machines. Screws are used to hold the pieces together. The wheel of a bicycle is a wheel and axle. The pedals are also examples of this simple machine. The pedals are attached to a lever that turns a pulley.

The position of a particular particle as a function of is given by r=(8.5t i+5.6j-2tk )m (a) Determine the particle’s velocity and acceleration as a function of time.(b) Find the instantaneous velocity and acceleration of the particle at t=3.0 s.

Answers

Answer:

use google to find answer

Explanation:

69 69 69 69 69 69

In straight line motion, if the velocity of an object is changing at a constant rate, then its position is _________ and its acceleration is___________: O changing: zero O changing; changing O constant and non-zero; constant and non-zero O None of the above

Answers

Answer:

None of the above

It should be position is changing and acceleration is constant.

Explanation:

Since the velocity is changing, this means the object is moving, so the position must also be changing.

Acceleration is the change in velocity in time, if this change of velocity happens at a constant rate, the acceleration must be constant too.

So, for example, if the velocity were to stay the same (not changing), acceleration would be zero, because there wouldn't be a change in time on the velocity.

So in this case the answer sould be position is changing and acceleration is constant. But this isn't in the options so the correct answer is "None of the above"

Final answer:

In straight line motion, if velocity changes at a constant rate, then the position is changing and the acceleration is constant and non-zero. This is defined under the principles of kinematics and implies that as the velocity alters constantly, the object is in motion, hence its position is changing.

Explanation:

In straight line motion, if the velocity of an object is changing at a constant rate, then its position is changing and its acceleration is constant and non-zero. This condition is defined under the laws of physics, more specifically, under the study of kinematics.

The acceleration is constant because you're considering a situation where velocity is changing at a constant rate. In this case, the change in velocity is the acceleration, which is a constant and not zero. This situation is described by the kinematic equations for constant acceleration.

The position is changing because the object is moving. A change in position over time constitutes motion, and in this case, because the velocity (the rate of change of position) is changing, the object's position cannot be constant.

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24-gauge copper wire has a diameter of 0.51 mm. The speaker is located exactly 4.27 m away from the amplifier. What is the minimum resistance of the connecting speaker wire at 20°C? Hint: How many wires are required to connect a speaker!Compare the resistance of the wire to the resistance of the speaker (Rsp = 8 capital omega)

Answers

Answer:

R = 8.94 10⁻² Ω/m, R_sp / R_total = 44.8

Explanation:

The resistance of a metal cable is

R = ρ L / A

The area of a circle is

A = π R²

The resistivity of copper is

ρ = 1.71 10⁻⁸ ohm / m

Let's calculate

R = 1.71 10⁻⁸ 4.27 / (π (0.51 10⁻³)²)

R = 8.94 10⁻² Ω/m

Each bugle needs two wire, phase and ground

The total wire resistance is

R_total = 2 R

R_total = 17.87 10⁻² Ω

Let's look for the relationship between the resistance of the bugle and the wire

R_sp / R_total = 8 / 17.87 10⁻²

R_sp / R_total = 44.8

Final answer:

The resistance of the speaker wire can be calculated using the formula for the resistance of a wire, taking into account the resistivity of copper, the length and thickness of the wire, and whether a single or pair of wires is used.

Explanation:

The question is asking you to find the minimum resistance of a copper wire given its diameter and length, plus the resistance of the speaker it's connected to. Resistance of a wire is calculated using the formula R=ρL/A, where R is the resistance, ρ (rho) is the resistivity of the material (in this case, copper), L is the length of the wire, and A is the cross-sectional area of the wire.

First, you need to find the area of the 0.51 mm diameter wire. The area (A) of a wire is given by the formula π(d/2)^2 where d is the diameter of the wire. After calculating the area, use the formula R=ρL/A to calculate the resistance. For copper wire at 20°C, ρ is approximately 1.68 × 10^-8 Ω·m. Substituting these values into the formula will give you the resistance of the wire in ohms.

Note: you may need to consider whether you have just a single wire or a pair, since two wires are typically required to connect a speaker. If a pair is used, each wire will carry half the current, which affects the total resistance.

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A 2.4-kg ball falling vertically hits the floor with a speed of 2.5 m/s and rebounds with a speed of 1.5 m/s. What is the magnitude of the impulse exerted on the ball by the floor