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
romanna [79]
3 years ago
9

A 25 kg child plays on a swing having support ropes that are 2.20 m long. A friend pulls her back until the ropes are 42◦ from t

he vertical and releases her from rest.
(a) What is the potential energy for the child just as she is released, compared to the potential energy at the bottom of the swing?

(b) How fast will she be moving at the bottom of the swing?

(c) How much work does the tension in the ropes do as the child swings from the initial position to the bottom of the swing? Hint: Think about the angle between the Tension force and the direction of motion.
Physics
1 answer:
Semmy [17]3 years ago
3 0

Answer:

A) P.E = 138.44 J

B) The velocity of swing at bottom, v = 3.33 m/s

C) The work done, W = -138.44 J

Explanation:

Given,

The mass of the child, m = 25 Kg

The length of the swing rope, L = 2.2 m

The angle of the swing to the vertical position, ∅ = 42°

A) The potential energy at the initial position ∅ = 42° is given by the relation

                                P.E = mgh joule

Considering h  = 0 for the vertical position

The h at ∅ = 42° is  h = L (1 - cos∅)

                               P.E = mgL (1 - cos∅)

Substituting the given values in the above equation

                               P.E = 25 x 9.8 x 2.2 (1 - cos42°)

                                      = 138.44 J

The potential energy for the child just as she is released, compared to the potential energy at the bottom of the swing is, P.E = 138.44 J

B) The velocity of the swing at the bottom.

At bottom of the swing the P.E is completely transformed into the K.E

                  ∴                 K.E = P.E

                                     1/2 mv² = 138.44

                                     1/2 x 25 x v² 138.44

                                            v² = 11.0752

                                             v = 3.33 m/s

The velocity of the swing at the bottom is, v = 3.33 m/s

C) The work done by the tension in the rope from initial position to the bottom

             Tension on string, T = Force acting on the swing, F

                      W=L\int\limits^0_\phi{F} \, d \phi

                             =L\int\limits^0_\phi{mg.sin \phi} \, d \phi

                            = -Lmg[cos\phi]_{42}^{0}

                            = - 2.2 x 25 x 9.8 [cos0 - cos 42°]

                            = - 138.44 J

The negative sign in the in energy is that the work done is towards the gravitational force of attraction.

The work done by the tension in the ropes as the child swings from the initial position to the bottom of the swing, W = - 138.44 J

You might be interested in
A mass of M-kg rests on a frictionless ramp inclined at 30°. A string with a linear mass density of μ=0.025" kg/m" is attached t
I am Lyosha [343]

Answer:

44.3 m/s

Explanation:

a) Draw a free body diagram of the mass M.  There are three forces:

Weight force mg pulling down,

Normal force N pushing perpendicular to the ramp,

and tension force T pulling parallel up the ramp.

Sum of forces in the parallel direction:

∑F = ma

T − Mg sin 30° = 0

T = Mg sin 30°

T = Mg / 2

Draw a free body diagram of the hanging mass m.  There are two forces:

Weight force mg pulling down,

and tension force T pulling up.

Sum of forces in the vertical direction:

∑F = ma

T − mg = 0

T = mg

Substitute:

mg = Mg / 2

m = M / 2

M = 2m

b) Velocity of a standing wave in a string is:

v = √(T / μ)

T = mg, and m = 5 kg, so T = (5 kg) (9.8 m/s²) = 49 N.  Therefore:

v = √(49 N / 0.025 kg/m)

v = 44.3 m/s

7 0
3 years ago
Two neutron stars are separated by a distance of 1.0 x 1012 m. They each have a mass of 1.0 x 1028 kg and a radius of 1.0 x 103
son4ous [18]

To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.

Gravitational potential energy can be defined as

PE = -\frac{GMm}{R}

As M=m, then

PE = -\frac{Gm^2}{R}

Where,

m = Mass

G =Gravitational Universal Constant

R = Distance /Radius

PART A) As half its initial value is u'=2u, then

U = -\frac{2Gm^2}{R}

dU = -\frac{2Gm^2}{R}

dKE = -dU

Therefore replacing we have that,

\frac{1}{2}mv^2 =\frac{Gm^2}{2R}

Re-arrange to find v,

v= \sqrt{\frac{Gm}{R}}

v = \sqrt{\frac{6.67*10^{-11}*1*10^{28}}{1*10^{12}}}

v = 816.7m/s

Therefore the  velocity when the separation has decreased to one-half its initial value is 816m/s

PART B) With a final separation distance of 2r, we have that

2r = 2*10^3m

Therefore

dU = Gm^2(\frac{1}{R}-\frac{1}{2r})

v = \sqrt{Gm(\frac{1}{2r}-\frac{1}{R})}

v = \sqrt{6.67*10^{-11}*10^{28}(\frac{1}{2*10^3}-\frac{1}{10^{12}})}

v = 1.83*10^7m/s

Therefore the velocity when they are about to collide is 1.83*10^7m/s

7 0
3 years ago
In your own words, explain what a field is in science. Use specific examples to support your explanation.
tresset_1 [31]

Answer:

Field, In physics, a region in which each point is affected by a force.

Explanation:

4 0
3 years ago
We have discovered some exoplanets that are still forming from a nebula. How might those planets change over time?
Rudik [331]
Based on several theories made by scientists, planets are formed because of the accumulation of gases and other particles that are attracted to each other. These accumulated gases form into clumps and eventually the clumps get bigger and turn into a big orbital mass. The exoplanets may experience change over time through the observance of its orbit in a particular axis, and if there are other debris that might affect the planet's continuous growth.
6 0
3 years ago
Convert 93.6 miles per hour. Convert this to kilometers per hour.
Readme [11.4K]

Answer:

150.6 km

Explanation:

One mile is about 1.61 km so multiply 93.6 by 1.6 which gives you above 150.6

3 0
2 years ago
Other questions:
  • Which of these temperatures is likely when a container of water at 20° C is mixed with water at 28° C?
    13·1 answer
  • An airplane heads northeast at an airspeed of 700 km/hr, but there is a wind blowing from the west at 60 km/hr. In what directio
    8·1 answer
  • _____ is a measure of the force of gravity pulling down on an object. it is measured in newtons (N), the common unit for measuri
    5·1 answer
  • What must be the acceleration of a train in order for it to stop from 12m/s in a distance of 541m?
    13·2 answers
  • What causes air to move recirculate from one place to another
    5·1 answer
  • What causes an electromagnet to create a magnetic field?
    15·1 answer
  • Hearing rattles from a snake, you make two rapid displacements of magnitude 1.8 m and 2.4m. Draw sketches, roughly to scale, to
    10·1 answer
  • Which is an example of current electricity?
    11·1 answer
  • 2 % of freshwater is locked in ______.
    10·1 answer
  • Because of the differences in physical properties, the lithosphere is effectively detached from the asthenosphere.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!