PHYSICS COLLEGE

You release a block from the top of a long, slippery inclined plane of length l that makes an angle θ with the horizontal. The magnitude of the block's acceleration is gsin(θ).1. For an x axis pointing down the incline and having its origin at the release position, derive an expression for the potential energy of the block-Earth system as a function of x. Suppose that the gravitational potential energy is measured relative to the ground at the bottom of the incline, UG(x=l)=0.Express your answer in terms of g and the variables m, l, x, and θ.(U^G=?)2. Use the expression you derived in the previous part to determine the speed of the block at the bottom of the incline. (Vx,f=?)Express your answer in terms of g and the variables m, l, and θ.

Answers

Answer 1

Answer:

Answer:

UG (x) = m*g*x*sin(Q)

Vx,f (x)= sqrt (2*g*x*sin(Q))

Explanation:

Given:

- The length of the friction less surface L

- The angle Q is made with horizontal

- UG ( x = L ) = 0

- UK ( x = 0) = 0

Find:

derive an expression for the potential energy of the block-Earth system as a function of x.

determine the speed of the block at the bottom of the incline.

Solution:

- We know that the gravitational potential of an object relative to datum is given by:

UG = m*g*y

Where,

m is the mass of the object

g is the gravitational acceleration constant

y is the vertical distance from datum to the current position.

- We will consider a right angle triangle with hypotenuse x and angle Q with the base and y as the height. The relation between each variable can be given according to Pythagoras theorem as follows:

y = x*sin(Q)

- Substitute the above relationship in the expression for UG as follows:

UG = m*g*x*sin(Q)

- To formulate an expression of velocity at the bottom we can use an energy balance or law of conservation of energy on the block:

UG = UK

- Where UK is kinetic energy given by:

UK = 0.5*m*Vx,f^2

Where Vx,f is the final velocity of the object @ x:

m*g*x*sin(Q) = 0.5*m*Vx,f^2

-Simplify and solve for Vx,f:

Vx,f^2 = 2*g*x*sin(Q)

Hence, Velocity is given by:

Vx,f = sqrt (2*g*x*sin(Q))

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A flat (unbanked) curve on a highway that has a radius of 50 m. A car rounds the curve. The car has mass 4,907 kg. The static coefficient of friction between the curve and the car is 0.35. What is the maximum speed of the car to prevent sliding?

Answers

Answer:

maximum speed of the car to prevent sliding is 13.1m/s

Explanation:

Given data

Radius of curve r=50m

Mass of car m=4907kg

Coefficient of friction u=0.35

Limiting for R=?

Hence limiting force R=ma

R=4907*9.81

R=48137.7N

We know that the force to overcome friction is

F=uR

Hence

F=0.35*48137.7

F=16848.2N

Centripetal force along the curve is given as

Fc=mv²/r

Fc = centripetal force

m = mass

v = velocity

r = radius

To solve for velocity we have to equate both force required to overcome friction and the centripetal force

Fc=mv²/r=F=uR

mv²/r=uR

Making velocity subject of formula we have

v²=u*r*R/m

v²=(0.35*50*48137.7)/4907

v²=842409.75/

v²=171.67

v=√171.67

v=13.1m/s

What If? Fluoride ions (which have the same charge as an electron) are initially moving with the same speed as the electrons from part (a) through a different uniform electric field. The ions come to a stop in the same distance d. Let the mass of an ion be M and the mass of an electron be m. Find the ratio of the magnitude of electric field the ions travel through to the magnitude of the electric field found in part (a). (Use the following as necessary: d, K, m, M, and e for the charge of the electron.)

Answers

Answer:

E₁ / E₂ = M / m

Explanation:

Let the electric field be E₁ and E₂ for ions and electrons respectively .

Force on ions = E₁ e where e is charge on ions .

Acceleration on ions a = E₁ e / M . Let initial velocity of both be u . Final velocity v = 0

v² = u² - 2as

0 = u² - 2 x E₁ e d / M

u² = 2 x E₁ e d / M

Similarly for electrons

u² = 2 x E₂ e d / m

Hence

2 x E₁ e d / M = 2 x E₂ e d / m

E₁ / E₂ = M / m

Final answer:

The ratio of the magnitude of the electric field the ions travel through to the magnitude of the electric field found in part (a) is M/m.

Explanation:

The ratio of the magnitude of the electric field the ions travel through to the magnitude of the electric field found in part (a) can be determined using the concept of mechanical energy conservation. Since the ions come to a stop, their initial kinetic energy must be equal to the work done by the electric field on them. The work done is given by the equation:

Work = Change in kinetic energy

The change in kinetic energy can be calculated using the formula:

Change in kinetic energy = (1/2)Mv2 - (1/2)mv2

where M and m are the masses of the ions and electrons respectively, and v is their initial speed. Solving for the ratio, we get:

Ratio = (1/2)M/(1/2)m = M/m

So, the ratio of the magnitude of electric field the ions travel through to the magnitude of the electric field found in part (a) is M/m.

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An athlete can exercise by making mechanical waves in ropes. What is themedium of these waves?
A. Energy
B. The rope
C. The athlete
D. Air

Answers

Answer:

It would be B. The Rope

Explanation:

I say this because the rope is transferring energy from one location to another. Now, I could be totally wrong on this but I think this is right lol.

Answer:

The answer is B the rope.

Hope this helps <3 ;)

A physicist is creating a computational model of a falling person before and after opening a parachute. What boundary conditions would be important here?the air resistance encountered as the person falls

the speed at which the person falls

the change in kinetic and potential energy

the location where potential energy is zero

Answers

Answer:

the location where potential energy is zero

Explanation:

Answer:

Air resistance

Explanation:

Air resistance encountered as the person falls

In a super-heater (A) pressure rises, temperature drops (B) pressure rises, temperature remains constant (C) pressure remains constant and temperature rises (D) both pressure and temperature remains constant

Answers

Answer:

i believe that it is d

Explanation:

Final answer:

In a super heater, the temperature of the steam rises while the pressure remains constant. This process helps to remove the last traces of moisture from the saturated steam.

Explanation:

In a super heater, the conclusion is that option (C) pressure remains constant and temperature rises is the correct choice. A super heater is a device used in a steam power plant to increase the temperature of the steam, above its saturation temperature. The function of the super heater is to remove the last traces of moisture (1 to 2%) from the saturated steam and to increase its temperature above the saturation temperature. The pressure, however, remains constant during this process because the super heater operates at the same pressure as the boiler.

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Experts in model airplanes develop a supersonic plane to scale, it moves horizontally in the air while it is conducting a flight test. The development team defines that the space that the airplane travels as a function of time is given by the function: e (t) = 9t 2 - 6t + 3 Determine what acceleration the scale airplane has (Second derivative).

Answers

Explanation:

e(t) = 9t² − 6t + 3

The velocity is the first derivative:

e'(t) = 18t − 6

The acceleration is the second derivative:

e"(t) = 18

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