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ANTONII [103]
3 years ago
5

A uniform solid disk and a uniform hoop are placed side by side at the top of an incline of height h. If they are released from

rest and roll without slipping, determine their speeds when they reach the bottom. (d = disk, h = hoop)
Physics
1 answer:
svlad2 [7]3 years ago
3 0

Answer:

) the uniform disk has a lower moment of inertia and arrives first.

Explanation:

(a) the uniform disk has a lower moment of inertia and arrives first.

(b) Let's say the disk has mass m and radius r, and

the hoop has mass M and radius R.

disk: initial E = PE = mgh

I = ½mr², so KE = ½mv² + ½Iω² = ½mv² + ½(½mr²)(v/r)² = (3/4)mv² = mgh

m cancels, leaving v² = 4gh / 3

hoop: initial E = Mgh

I = MR², so KE = ½MV² + ½(MR²)(V/R)² = MV² = Mgh

M cancels, leaving V² = gh

Vdisk = √(4gh/3) > Vhoop = √(gh)

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Two identical cows fell into a muddy hole. One fell on its side and the other fell on its feet.Which one sank furthest into the
olga_2 [115]

Answer:

The one which falls on feet.

Explanation:

Because it exerts higher pressure as

P= F/ A

Larger the area less will be the pressure and less is the area larger will be the pressure.

8 0
3 years ago
A crate slides down a ramp that makes a 20o angle with the ground. To keep the crate moving at a steady speed, Paige pushes back
cupoosta [38]

Answer:

-223.64684 J

Explanation:

F = Force that is applied to the crate = 68 N

s = Displacement of the crate = 3.5 m

\theta = Angle between the force and displacement vector = (180-20)

Work done is given by

W=Fscos\theta\\\Rightarrow W=68\times 3.5\times cos(180-20)\\\Rightarrow W=-223.64684\ J

The work that Paige does on the crate is -223.64684 J

6 0
3 years ago
When two resistors are wired in series with a 12 V battery, the current through the battery is 0.33 A. When they are wired in pa
MA_775_DIABLO [31]

Answer:

If R₂=25.78 ohm, then R₁=10.58 ohm

If R₂=10.57 then R₁=25.79 ohm

Explanation:

R₁ = Resistance of first resistor

R₂ = Resistance of second resistor

V = Voltage of battery = 12 V

I = Current = 0.33 A (series)

I = Current = 1.6 A (parallel)

In series

\text{Equivalent resistance}=R_{eq}=R_1+R_2\\\text {From Ohm's law}\\V=IR_{eq}\\\Rightarrow R_{eq}=\frac{12}{0.33}\\\Rightarrow R_1+R_2=36.36\\ Also\ R_1=36.36-R_2

In parallel

\text{Equivalent resistance}=\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}\\\Rightarrow {R_{eq}=\frac{R_1R_2}{R_1+R_2}

\text {From Ohm's law}\\V=IR_{eq}\\\Rightarrow R_{eq}=\frac{12}{1.6}\\\Rightarrow \frac{R_1R_2}{R_1+R_2}=7.5\\\Rightarrow \frac{R_1R_2}{36.36}=7.5\\\Rightarrow R_1R_2=272.72\\\Rightarrow(36.36-R_2)R_2=272.72\\\Rightarrow R_2^2-36.36R_2+272.72=0

Solving the above quadratic equation

\Rightarrow R_2=\frac{36.36\pm \sqrt{36.36^2-4\times 272.72}}{2}

\Rightarrow R_2=25.78\ or\ 10.57\\ If\ R_2=25.78\ then\ R_1=36.36-25.78=10.58\ \Omega\\ If\ R_2=10.57\ then\ R_1=36.36-10.57=25.79\Omega

∴ If R₂=25.78 ohm, then R₁=10.58 ohm

If R₂=10.57 then R₁=25.79 ohm

6 0
3 years ago
Which of the following statements is true based on the law of conservation
ipn [44]

Answer:

B

Explanation:

The mass of something before it's been processed is the same as it's mass after the process.

7 0
3 years ago
Let the masses of blocks A and B be 4.50 kg and 2.00 kg , respectively, the moment of inertia of the wheel about its axis be 0.4
Free_Kalibri [48]

Answer:

Accelerations of both the sides is 0.6125 m/s^{2}, A moves downwards whereas B moves upwards.

\alpha=6.125 rad/s^{2}

Tension on side A = 4.5 × g= 44.1 m/s^{2}

Tension on side B= 2.0 × g=  19.6 m/s^{2}

Explanation:

As both, the blocks A and B are attached due to the constraint they can only possess a single acceleration a.

Observe the figure attached, let the tension with Block A be T_{2} and the tension attached with Block B be T_{1} .

Tensions will be only be due to the weight of the blocks as no other force is present.

T_{2} = 4.5 × g= 44.1 m/s^{2}

T_{1} = 2.0 × g=  19.6 m/s^{2}

Now, lets make a torque equation about the center of the wheel and find the alpha

T_{2}×R- T_{1}×R= MI( Moment of Inertia of Wheel)× Alpha

where, R= Radius of the wheel=0.100m  and

           Alpha(\alpha)= Angular acceleration of the wheel

MI of the wheel= 0.400 kg/m^{2}

(44.1-19.6)R=0.400\alpha

\alpha = \frac{24.5 * 0.100}{0.400}

\alpha=6.125 rad/s^{2}

Acceleration = R ×\alpha

                    = 0.1 * 6.125

                    =0.6125 m/s^{2}

Accelerations of both the sides is 0.6125 m/s^{2}, A moves downwards whereas B moves upwards.

7 0
3 years ago
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