1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
N76 [4]
3 years ago
14

g A 1.5 kg block is initially at rest on a horizontal frictionless surface when a horizontal force along an x axis is applied to

the block. The force is given by , where x is in meters and the initial position of the block is x 0. (a) What is the kinetic energy of the block as it passes through x _ 2.0 m? (b) What is the maximum kinetic energy of the block between x _ 0 and x_ 2.0 m?
Physics
1 answer:
lidiya [134]3 years ago
3 0

Answer:

(a). The kinetic energy is 5.33 J

(b). The maximum kinetic energy is 5.33 J.

Explanation:

Given that,

Mass of block = 1.5 kg

Suppose the force is

F=(4-x^2)i\ N

(a). We need to calculate the kinetic energy of the block

Using work energy theorem

\Delta k=W_{f}

K(x)=\int_{0}^{x}{4-x^2}dx

K(x)=4x-\dfrac{x^3}{3}....(I)

Now put the value of x in equation

K(x)=4\times2-\dfrac{2^3}{3}

K(x)=5.33\ J

The kinetic energy is 5.33 J

For K to be minimum

\dfrac{dK}{dx}=0

4-\dfrac{3x^2}{3}=0

4-x^2=0

x=2

(b). We need to calculate the maximum kinetic energy of the block

For K to be maximum

\dfrac{d^2K}{dx^2}=0

\dfrac{d^2K}{dx^2}=0-2x

Put the value of x

\dfrac{d^2K}{dx^2}=-4

Now put the value of x in equation (I)

K(x)=4\times2-\dfrac{2^3}{3}

K(x)=5.33\ J

The maximum kinetic energy is 5.33 J

Hence, (a). The kinetic energy is 5.33 J

(b). The maximum kinetic energy is 5.33 J.

You might be interested in
A 35 kg child slides down a playground slide at a constant speed. The slide has a height of 3.8 m and is 8.0 m long. Find the ma
ad-work [718]

Answer:

The magnitude of the kinetic frictional force acting on the child is 162.93 N

Explanation:

Given;

mass of the child, m = 35 kg

height of the slide, h = 3.8 m

length of the slide, d = 8.0 m

The change in thermal energy associated with the kinetic frictional force is calculated as follows;

\Delta E_{th} + \Delta K.E + \Delta U = 0\\\\\Delta E_{th} + (\frac{1}{2} mv_f^2 - \frac{1}{2} mv_i^2) + (mgh_f - mgh_i) =0\\\\since \ the \ speed \ is \ constant, \ v_f = v_i \ and \ \Delta K.E = 0\\\\Also, \ final \ height \ , h _f= 0\\\\\Delta E_{th} - mgh_i = 0\\\\\Delta E_{th} = mgh_i\\\\\Delta E_{th} = 35 \times9.8 \times 3.8\\\\\Delta E_{th} = 1303.4 \ J

The magnitude of the kinetic frictional force that produced this thermal energy is calculated from the work done by frictional force;

\Delta E_{th} = F \times d\\\\F = \frac{\Delta E_{th} }{d} \\\\F = \frac{1303.4}{8} \\\\F = 162.93 \ N

Therefore, the magnitude of the kinetic frictional force acting on the child is 162.93 N

8 0
3 years ago
If a woman pushes a box for 3 meters and does 600J of work, how much work does the box do?
kykrilka [37]
Energy = force x distance
600 J = force x 3 m
force = 200 N

Work = force x distance
Work = 200 N x 3 m
Work = 600 J

Therefore work done = energy
5 0
4 years ago
NEED HELP THIS IS DUE IN 30 MINUTES
11111nata11111 [884]

-- The total distance between the towns = 460 km.

-- For the first 3 hours, he travels at an average speed of 60 km/hr.  During that time, he covers (60 km/hr) x (3 hrs) = 180 km.

-- At that point, he still has (460km - 180km) = 280 km to go.

-- If he drives that 280km at an average speed of 70 km/hr, it'll take him (280km)/(70km/hr) = 4 hrs to cover it.

-- His total time for the whole trip is (3 hours for the first part) + (4 hours for the last part) = <em>7 hours</em>.

8 0
3 years ago
How many more neutrons are in a I SOTOPE of copper-14 than in standard carbon atom
sweet-ann [11.9K]

Answer:

2 more neutrons

Explanation:

To obtain the answer to the question, let us calculate the number of neutrons in carbon–14 and standard carbon (i.e carbon–12). This can be obtained as follow:

For carbon–14:

Mass number = 14

Proton number = 6

Neutron number =?

Mass number = Proton + Neutron

14 = 6 + Neutron

Collect like terms

14 – 6 = Neutron

8 = Neutron

Neutron number = 8

For carbon–12:

Mass number = 12

Proton number = 6

Neutron number =?

Mass number = Proton + Neutron

12 = 6 + Neutron

Collect like terms

12 – 6 = Neutron

6 = Neutron

Neutron number = 6

SUMMARY:

Neutron number of carbon–14 = 8

Neutron number of carbon–12 = 6

Finally, we shall determine the difference in the neutron number. This can be obtained as follow:

Neutron number of carbon–14 = 8

Neutron number of carbon–12 = 6

Difference =?

Difference = (Neutron number of carbon–14) – (Neutron number of carbon–12)

Difference = 8 – 6

Difference = 2

Therefore, carbon–14 has 2 more neutrons than standard carbon (i.e carbon–12)

3 0
3 years ago
PLEASE HELP ASAP! This is an emergency!
dsp73
1. A
2. B 
3. C
4. C
that's all I've got! Im sorry! 
8 0
3 years ago
Read 2 more answers
Other questions:
  • A standard quantity of a physical property used as a factor to compare other occurring quantities of that property is called a(n
    9·1 answer
  • A wave has a low speed but a high frequency. What can you infer about its wavelength?
    6·1 answer
  • You pull with a force of 255 N on a piece of luggage of mass 68 kg, but it does not move. If the coefficient of friction between
    15·2 answers
  • Corra is playing with a basketball with her friends after school. She takes a shot and throws it high into the air. As the ball
    10·1 answer
  • Steam at 1 atm and 100C is flowing across a 5-cm-OD tube at a velocity of 6 m/s. Estimatethe Nusselt number, the heat transfer c
    8·1 answer
  • A grain silo is shown below:grain silo formed by cylinder with radius 5 feet and height 175 feet and a half sphere on the topwha
    8·1 answer
  • Power output of an engine is with work (w= 60,000J) during 60 s Calculate the power of this work?
    5·1 answer
  • What type of process occurs at constant pressure
    10·2 answers
  • Physical systems that serve as framework for city growth are called __________.
    12·2 answers
  • Two particles are 15 meters apart.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!