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anyanavicka [17]
2 years ago
8

You have a pumpkin of mass m and radius r. the pumpkin has the shape of a sphere, but it is not uniform inside so you do not kno

w its moment of inertia. in order to determine the moment of inertia, you decide to roll the pumpkin down an incline that makes an angle θ with the horizontal. the pumpkin starts from rest and rolls without slipping. when it has descended a vertical height h, it has acquired a speed of v = √(5gh/4).
Physics
1 answer:
geniusboy [140]2 years ago
8 0
<span>As it is descended from a vertical height h, The lost Potential Energy = Mgh The gained Kenetic Energy = (1/2)Mv^2; The rotational KE = (1/2)Jw^2 The angular speed w = speed/ Radius = v/R So Rotational KE = (1/2)Jw^2 = (1/2)J(v/R)^2; J is moment of inertia Now Mgh = (1/2)Mv^2 + (1/2)J(v/R)^2 => 2gh/v^2 = 1 + (J/MR^2) As v = (5gh/4)^1/2, (J/MR^2) = 2gh/v^2 - 1 => (J/MR^2) = (8gh/5gh) - 1 so (J/MR^2) = 3/5 and therefore J = (3/5)MR^2.</span>
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Max and Jimmy want to jump on a trampoline. Max begins jumping in a steady pattern, making small waves in the trampoline. Jimmy
mylen [45]

Answer:

x_total = (A + B) cos (wt + Ф)

we have the sum of the two waves in a phase movement

Explanation:

In this case we can see that the first boy Max when he enters the trampoline and jumps creates a harmonic movement, with a given frequency. When the second boy Jimmy enters the trampoline and begins to jump he also creates a harmonic movement. If the frequency of the two movements is the same and they are in phase we have a resonant process, where the amplitude of the movement increases significantly.

         Max

               x₁ = A cos (wt + Ф)

         Jimmy

              x₂ = B cos (wt + Ф)

         

total movement

             x_total = (A + B) cos (wt + Ф)

 Therefore we have the sum of the two waves in a phase movement

8 0
2 years ago
What is Otter's average velocity over his entire trip when it takes him 2 minutes to walk 100 meters north and another 1 minute
Leya [2.2K]

Answer:

0.50m/s

Explanation:

Average velocity is the change in displacement of a body with respect to time.

Velocity = ∆S/∆t

∆S = 100m - 70m

∆S = 30m

∆t = 2min - 1 min

∆t = 1min = 60secs

Substitute the given parameters into the formula for velocity

Velocity = 30m/60s

Velocity = 1/2 m/s

Average Velocity = 0.5m/s

7 0
2 years ago
A proton of mass mp is released from rest just above the lower plate and reaches the top plate with speed vp. An electron of mas
vodka [1.7K]

Answer:

v_e=\sqrt{\frac{m_pv_p^2}{m_e}}

Explanation:

You can consider that the force that acts over the proton is the same to the force over the electron. This is because the electric force is given by:

F=qE

F_p=F_e

where E is the constant electric field between the parallel plates, and is the same for both electron and proton. Also, the charge is the same.

by using the Newton second law for the proton, and by using kinematic equation for the calculation of the acceleration you can obtain:

m_pa_p=qE\\\\a_p=\frac{v_p^2}{2d}\\\\\frac{m_pv_p^2}{2d}=qE

(it has been used that vp^2 = v_o^2+2ad) where d is the separation of the plates, ap the acceleration of the proton, vp its velocity and mp its mass.

By doing the same for the electron you obtain:

\frac{m_ev_e^2}{2d}=qE

we can equals these expressions for both proton and electron, because the forces qE are the same:

\frac{m_pv_p^2}{2d}=\frac{m_ev_e^2}{2d}\\\\v_e=\sqrt{\frac{m_pv_p^2}{m_e}}

4 0
2 years ago
When the Glen Canyon hydroelectric power plant in Arizona is running at capacity, 690 m3 of water flows through the dam each sec
bixtya [17]

Answer:

1340.2MW

Explanation:

Hi!

To solve this problem follow the steps below!

1 finds the maximum maximum power, using the hydraulic power equation which is the product of the flow rate by height by the specific weight of fluid

W=αhQ

α=specific weight for water =9.81KN/m^3

h=height=220m

Q=flow=690m^3/s

W=(690)(220)(9.81)=1489158Kw=1489.16MW

2. Taking into account that the generator has a 90% efficiency, Find the real power by multiplying the ideal power by the efficiency of the electric generator

Wr=(0.9)(1489.16MW)=1340.2MW

the maximum possible electric power output is 1340.2MW

3 0
2 years ago
A 1150 kg car is on a 8.70° hill. using x-y axis tilted down the plane, what is the x-component of the weight?
Fed [463]
I assume the x-y axis are tilted such that the x-axis is parallel to the surface of the hill while the y-axis is perpendicular to it.

In this case, the x-component of the weight is given by:
W_x =mg \sin \theta
where
m is the mass of the car
g is the acceleration of gravity
\theta is the angle of the hill

Substituting numbers into the formula, we find
W_x=(1150 kg)(9.81 m/s^2)(\sin 8.70^{\circ})=1706 N
6 0
2 years ago
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