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Mars2501 [29]
2 years ago
5

An object moves in one dimension according to the function x(t)=13at3, where a is a positive constant with units of ms3. During

this motion, a force F⃗ =−bv is exerted on the object, where v is the object’s velocity and b is a constant with units of kgs. Which of the following expressions will yield the amount of energy dissipated by this force during the time interval from t=0 and t=T ?
A− 19ba2T5
B− 15ba2T5
C− 13ba2T5
D− ba2T5
Physics
1 answer:
9966 [12]2 years ago
7 0

Answer:

B) 1/5 ba^2 T^5

Explanation:

The dissipated energy is given by the work done over the object by the force F=-bv. The work is given by the following formula:

dW=Fdx

you derivative the function f(x) and replace v by the derivative dx/dt you obtain:

v=\frac{dx}{dt}=at^2\\\\dx=at^2dt\\\\W=\int_0^{T} Fdx=-\int_0^Tvbdx=-\int_0^Tb(at^2)(at^2dt)\\\\W=-ba^2\frac{T^5}{5}=-\frac{1}{5}ba^2T^5

hence, the dissipated energy is 1/5 ba^2 T^5

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If a force always acts perpendicular to an object's direction of motion, that force cannot change the object's kinetic energy.
laiz [17]
This is very good conceptual question and can clear your doubts regarding work-energy theorem.
Whenever force is perpendicular to the direction of the motion, work done by that force is zero.
According to work-energy theorem,
Work done by all the force = change in kinetic energy.

here, work done = 0.
Therefore, 
0=change in kinetic energy
This means kinetic energy remains constant.
Hope this helps
5 0
2 years ago
4.A photon of green light strikes an unknown metal and an electron is emitted. The voltage is set to 2 volts. The electron canno
Anarel [89]
4) The correct answer is:
<span>B. An electron will be emitted in the second experiment, but it cannot be determined whether it will reach the second plate. 

In fact, violet light has higher frequency than green light. This means that photons of violet light carry more energy than photons of green light (remember that the energy of a photon is proportional to its frequency: </span>E=hf)<span>, so when they hit the surface of the metal, more energy is transferred to the electrons. The electron was already emitted with green light, so it must be emitted also with violet light, given the more energy transferred. The electron will also have more kinetic energy when hit by violet light, however, we cannot determine if it will reach the second plate, since we don't know how much energy has been used to extract the electron from the metal (in fact, we don't know the work function of the metal, i.e. the energy needed to extract the electron)


3)  The correct answer is
</span><span>A. Violet light will cause electrons to be emitted at greater velocities than those removed by green light.

In fact, </span>violet light has higher frequency than green light. This means that photons of violet light carry more energy than photons of green light (remember that the energy of a photon is proportional to its frequency: E=hf), so when they hit the surface of the metal, more energy is transferred to the electrons. Therefore, the emitted electrons will have on average greater energy (and so, greater velocity) than those removed by green light.
3 0
2 years ago
A negative charge of -0.550 μC exerts an upward 0.900-N force on an unknown charge that is located 0.300 m directly below the fi
allochka39001 [22]

Answer:

a.   q2 = 16.4μC, positive charge

b.   F = 0.900N

c.   downward

Explanation:

a. In order to calculate the charge of the unknown charge you use the following formula, for the electric force between two charges:

F_e=k\frac{q_1q_2}{r^2}            (1)

k: Coulomb's constant = 8.98*10^9Nm^2/C^2

r: distance between the charges = 0.300m

q1: charge 1 = -0.550 μC = 0.550*10^-6C

q2: charge 2 = ?

Fe: electric force = 0.900N

The force exerted in the second charge points upward, then, the sign of the second charge is positive because this charge is getting closer to the first one.

You solve the equation (1) for the second charge ans replace the values of the other parameters:

q_2=\frac{r^2F_e}{kq_1}=\frac{(0.300m)^2(0.900N)}{(8.98*10^9Nm^2/C^2)(0.550*10^{-6}C)}\\\\q_2=1.64*10^{-5}C\\\\q_2=16.4*10^{-6}C=16.4*10\mu C

The values of the second charge is 1.64 μC

b. By the third Newton Law, you have that the force exerted in the second charge is equal to the force exerted by the first charge on the second one.

The force exerted on the first charge is 0.900N

c. The charges are attracting between them, then, the force exerted on the first charge is pointing downward.

3 0
2 years ago
Given a die, would it be more likely to get a single 6 in six rolls, at least two 6s in twelve rolls, or at least one-hundred 6s
vichka [17]

Answer:

Explanation:

In first case we are interested in one time 6 in six rolls

Thus probability = number of chances required/Total chances

= 1/6

Similarly in the second case probability = 2/12 = 1/6

In the same way in last case probability = 100/600 = 1/6

The probability is the same . Thus all the cases has equal chances  

4 0
2 years ago
A wooden piece is made in different shapes take length (l) = radius (r) = 2m Calculate its volume as a:
In-s [12.5K]

This question deals with the volume of different shapes.

a) volume of the sphere is "33.51 m³".

b) volume of the cylinder is "25.13 m³".

a)

The volume of a sphere is given by the following formula:

Volume = \frac{4}{3}\pi r^3\\\\Volume = \frac{4}{3}\pi (2\ m)^3

<u>Volume = 33.51 m³</u>

<u />

b)

The volume of a cylinder is given by the following formula:

Volume = \pi r^2l\\\\Volume =\pi (2\ m)^2(2\ m)

<u>Volume = 25.13 m³</u>

<u />

Learn more about <em>volume </em>here:

brainly.com/question/16686115?referrer=searchResults

The attached picture shows the formulae of the <em>volume</em> of different shapes.

7 0
2 years ago
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