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AfilCa [17]
3 years ago
14

The 3.0 kg object below is released from rest at a height of 5.0 m on a curved frictionless ramp. At the foot of the ramp is a s

pring of force constant k = 500 N/m. The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest. a) Find x. b) what happens to the object after it comes to rest?
Physics
1 answer:
scoray [572]3 years ago
7 0

Answer:

a) The compressing distance is 0.8 m.

b) After the object comes to rest, it will be released with an initial speed of 7.1 m/s and will reach a height of 5.0 m.

Explanation:

Hi there!

a)Initially, the object has only gravitational potential energy that is calculated as follows:

PE = m· g · h

Where:

PE = potential energy.

m = mass.

g = acceleration due to gravity.

h = height.

Then:

PE = 3.0 kg · 9.8 m/s² · 5.0 m = 1.5 × 10² J

When the object reaches the spring and compresses it, all that potential energy is converted into elastic potential energy (there is no energy dissipation as heat because there is no friction). The elastic potential energy is calculated as follows:

EPE = 1/2 · k · x²

Then, the elastic potential energy is equal to the initial gravitational energy:

PE = EPE = 1.5 × 10² J = 1/2 · 500 N/m · x²

Solving for x:

1.5 × 10² Nm / (1/2 · 500 N /m) = x²

0.6 m² = x²

x = 0.8 m

The compressing distance is 0.8 m.

b) After the object comes to rest, the object will be released with a kinetic energy equal to the elastic potential energy. We can calculate the initial velocity of the object after it is released with the following equation:

KE = 1/2 · m · v²

Where:

KE = kinetic energy.

m = mass.

v = speed.

Since initially EPE = KE:

1.5 × 10² J = 3.0 kg · v²

√( 1.5 × 10² J / 3.0 kg) = v

v = 7.1 m/s

Then, after the object comes to rest, it will be released with an initial speed of 7.1 m/s and will reach a height of 5.0 m.

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7. Calculations.
kotykmax [81]

Answer:

5 ms-2

Explanation:

F = ma

F = 100N

m = 20kg ( you should make sure the unit is kg before you answer the question)

100 = 20a

a = 100÷ 20

a = 5 ms-2

4 0
3 years ago
An object is placed 4.0 cm to the left of a convex lens with a focal length of +8.0 cm . Where is the image of the object?
Serjik [45]

The image of the object is 8cm to the left of the lens (D)

<h3></h3>

What is the image of an object?

The image of an object is said to be the location where light rays from that object intersect with a mirror by reflection.

It is calculated thus:

1÷v = 1÷f - 1÷u

<h3>How to calculate the image of an object</h3>

From the formula

1÷v = 1÷f - 1÷u

<h3>Where </h3>

V = image distance fromthe object

U = object

f = focal length

Substitute the values

1÷v = 1÷8 - 1÷ 4

1÷v = - 1÷8

Make v the subject of formula

v = -8cm

Therefore, the image of the object is 8cm to the left of the lens (D)

Learn more on focal length here:

brainly.com/question/25779311

#SPJ1

6 0
2 years ago
2. If you want 0. 250 a (250 milliamps) to flow around a circuit with a resistance of 400 ohms, what voltage do you need?
grigory [225]

Answer:

0.000625 V

Explanation:

The formula linking current , resistance and voltage is :

V = I/R

Voltage = Current / Resistance

Now we substitute values given in question :

Voltage = 0.250 / 400

Voltage (V) = 0.000625

Our final answer is 0.000625 V

Hope this helped and have a good day

5 0
1 year ago
One mole of an ideal gas does 3000 J of work on its surroundings as it expands isothermally to a final pressure of 1.00 atm and
taurus [48]

Answer:

(a) Initial volume will be 7.62 L

(b) Final temperature will be 303.85 K

Explanation:

We have given one mole of ideal gas done 3000 J

So work done W = 3000 J

Let initial volume is V_1 and initial pressure P_1=1atm ( As pressure is constant )

Final volume V_2=25L = 0.025 m^3

Number of moles n = 1

(B) From ideal gas of equation we know that PV=nRT

So 1.01\times 10^5\times0.025=1\times 8.31\times T

T = 303.85 Kelvin

(B) For isothermal process work done is equal to

W=nRTln\frac{V_2}{V_1}

3000=1\times 8.314\times 303.85\times ln\frac{0.025}{V_1}

ln\frac{0.025}{V_1}=1.1881

\frac{0.025}{V_1}=3.2808

V_2=0.00846m^3=7.62L

So initial volume will be 7.62 L

5 0
3 years ago
It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral mo
bezimeni [28]

Radius of circle of spiral path = 6 m

Time period = 5 s

So the total length of the path = 2 \pi R

distance = 2 \pi R

distance = 2 \pi *6

distance = 12\pi

time taken by bird to cover the distance = 5 s

so the speed of the bird = distance / time

v = \frac{distance}{time}

v = \frac{12\pi}{5}

v = 7.54 m/s

so the tangential speed in horizontal direction = 7.54 m/s

vertical velocity by which it is rising upwards = 3 m/s

so the angle with the horizontal for net speed is given as

\theta = tan^{-1}\frac{v_y}{v_x}

\theta = tan^{-1}\frac{3}{7.54}

\theta = 21.7 degree

so velocity vector will make 21.7 degree with the horizontal

8 0
3 years ago
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