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Dmitry_Shevchenko [17]
3 years ago
10

Calculate the translational speed of a cylinder when it reaches the foot of an incline 7.35 m high. assume it starts from rest a

nd rolls without slipping.
Physics
1 answer:
allochka39001 [22]3 years ago
6 0
The total kinetic energy will be equivalent to the potential energy;
The total kinetic energy is given by the sum of transitional kinetic energy and the rotational kinetic energy.
Rotational kinetic energy
I= 1/2mR², but rotational energy =1/2 I w² 
Thus  rotational energy is equal to 1/4 mR²w², which is equivalent to 
 = 1/4 mv² since v= wR
Thus;
Total kinetic energy = 1/2 mv² + 1/4 mv²
hence;
 Mgh = 3/4 mv²
  gh = 3/4 v² ( assuming g = 9.81 m/s²)
   72.1035 = 3/4 v²
v = 9.805
    = 9.805 m/s
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A tank contains 150 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pu
nikitadnepr [17]

Answer:

The number A(t) of grams of salt in the tank at time t is A(t) = 150 - 110 e^{-\frac{t}{50} }

Explanation:

Knowing

\frac{dA}{dt} = Rin - Rout

First we have to find the Rin and Rout

Rin = (concentration of the salt inflow) * (input rate of brine)

Rin = 1 g/L * 3 L/min = 3 g/L

Rout = (concentration of the salt outflow) * (output rate of brine)

Rout = (\frac{A(t)}{150} g/L) * (3 L/min) = \frac{A(t)}{50} g/min

Substituting this results

\frac{dA}{dt} = 3 - \frac{A(t)}{50} --> \frac{dA}{dt} + \frac{1}{50} A(t)  = 4

Thus, integration factors is

e^{ \int\limits^._. {\frac{1}{50} } \, dt } = e^{\frac{t}{50} }

e^{\frac{t}{50} } \frac{dA}{dt} + \frac{1}{50} e^{\frac{t}{50} A(t) = 4 e^{\frac{t}{50} }

e^{\frac{t}{50} } A(t) = \int\limits^._. {3 e^{\frac{t}{50} } } \, dt\\ \\A(t) = 150 + c e^{-\frac{t}{50} }

Applying the initial conditions

A(0) = 40

c = 150 - 40 = 110

Now, substitute this result in the solution to get

A(t) = 150 - 110 e^{-\frac{t}{50} }

8 0
4 years ago
The Cajun Cliffhanger at Great AMerica is a ride in which occupants line the perimeter of a cylinder and spin in a circle at a h
12345 [234]

Explanation:

Centripetal Force is the force that keeps the object's rotation in a circular path and it's always directed towards the center of rotation. Mathematically, it is given as,

F_{c} = \frac{mv^{2} }{r}

From this equation it can be concluded that the centripetal force is proportional to the product of mass and the square of velocity. It is inversely proportional to the object's distance from the center.

Now in the above mentioned case, when the cylinder begins spinning very rapidly and it's speed becomes double. Then by applying the above equation we conclude that " the force will be increased four times if the speed is doubled as it is proportional to square of speed."

5 0
3 years ago
A couple of ice cubes float in a glass of water. Will the water level in the glass
taurus [48]

Answer:

Yes, the water level in the glass will decrease as the icecubes melt, this is a due to water displacement.

6 0
3 years ago
Calculate the force of an object shot in the air with a mass of 2 kg and an acceleration of 9.81 m/s2.
Helen [10]

Answer:

Force = 19.62 Newton

Explanation:

Given the following data;

Mass = 2kg

Acceleration = 9.81 m/s²

To find the force;

Newton's Second Law of Motion states that the acceleration of a physical object is directly proportional to the net force acting on the physical object and inversely proportional to its mass.

Mathematically, it is given by the formula;

Force = mass * acceleration

Substituting into the formula, we have;

Force = 2 * 9.81

Force = 19.62 Newton

4 0
3 years ago
Bending the stick stretches the chemical bonds holding the stick's atoms together, which provides a source of elastic energy.
Tema [17]

Answer:

true

Explanation:

3 0
3 years ago
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