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
Goryan [66]
3 years ago
14

A cart loaded with bricks has a total mass of 22.2 kg and is pulled at constant speed by a rope. The rope is inclined at 27.5 ◦

degrees above the horizontal and the cart moves 24 m on a horizontal floor. The coefficient of kinetic friction between ground and cart is 0.32. The acceleration of gravity is 9.8 m/s 2 . How much work is done on the cart by the rope?
Physics
2 answers:
Sedaia [141]3 years ago
8 0

Answer:

W=1432.27\ J

Explanation:

Given:

  • mass of the cart, m=22.2\ kg
  • inclination of rope above the horizontal, \theta=27.5^{\circ}
  • displacement of cart, s= 24\ m
  • coefficient of kinetic friction, \mu_k=0.32

<u>We find the force acting in the direction of the rope responsible for motion of the cart:</u>

f=\mu_k.R ................................................(1)

Here normal reaction R:

F.sin\theta+R=m.g ........................................(2)

<u>Now since the body is moving with a constant velocity:</u>

∴ Kinetic Frictional force = applied force

f=F

\mu_k.R=F.cos\theta

R=\frac{F.cos\theta}{\mu_k} ................................................(3)

<u>Putting the value of R from eq. (3) into eq. (2)</u>

F.sin\theta+\frac{F.cos\theta}{\mu_k}=m.g

F=m.g\div (sin\theta+\frac{cos\theta}{\mu_k})

F=22.2\times 9.8\div (sin 27.5+\frac{cos27.5}{0.32})

F=67.28\ N is the force applied along the rope.

<u>Now the work done by the rope:</u>

W=F.s\ cos\theta

W=67.28\times 24\times cos\ 27.5

W=1432.27\ J

musickatia [10]3 years ago
7 0

Answer:

W = 1.432 KJ

Explanation:

given,

mass = 22.2 Kg

angle of the rope = 27.5°

distance on the ground = 24 m

kinetic friction= μ = 0.32

acceleration due to gravity, g = 9.8 m/s²

Work done = ?

W = F d cosθ

a = 0 because it is moving with constant speed

equating all the forces acting  in x direction

F cosθ = F friction = μN  

equating all the forces acting  in y direction

F sinθ + N -mg =0

now,

N = mg - F sinθ

putting value of N

F cosθ = μ mg -μ F sinθ

F (cosθ + μsinθ ) = μ mg

F = \dfrac{\mu mg}{cos\theta + \mu sin\theta}

F = \dfrac{0.32 \times 22.2 \times 9.8}{cos 27.5^0+0.32 \times sin27.5^0}

F =67.28 N

now,

W=F d cosθ

W =67.28 x 24 x cos(27.5)

W =1432.27 J

W = 1.432 KJ

You might be interested in
¿Por que una una tapa pequeña de agua purificada se mantiene quieta por más tiempo sobre una rampa, en comparación al tiempo red
shusha [124]

Answer:

Esto sucede principalmente por el movimiento rotacional de las ruedas del carrito.

Como sabemos, existen dos tipos de coeficientes de fricción, el estacionario y el cinético.

En principio, la tapa se mantendrá quieta por que no tendrá la suficiente fuerza como para vencer al coeficiente de fricción estático, por lo que no podrá moverse hasta que esta reciba un pequeño impulso, como puede ser una pequeña corriente de aire. (asumo que la superficie curva de la tapita es la que esta en contacto con la rampa)

(Voy a simplificar el movimiento rotacional, pero creo que es suficiente para explicar la situación)

Ahora, en el carrito, las ruedas están conectadas a un eje.

La fuerza gravitatoria podemos pensarla que esta arriba de este eje, mas o menos en el centro del carrito, y esta fuerza intentara que el carrito baje de la rampa (lo mismo pasa para la tapita), pero a diferencia de la tapita, esta fuerza es aplicada a una distancia dada del eje (o del centro de las rueditas) lo que podemos pensar que funciona como una palanca, amplificando así la fuerza, por lo que esta vez el rozamiento estático podrá detener la superficie de la rueda que esta en contacto con el suelo, pero cuanto el centro de masa se mueva un poco, el punto de contacto entre la rueda y el suelo se moverá, de esta manera aparece lo que llamamos movimiento rotacional (si no hubiera fricción, las ruedas simplemente deslizarían sobre la rampa) que le permite al carrito ignorar en parte al coeficiente de fricción estático.

Otro factor importante, es que las tapitas suelen tener una superficie rugosa y un centro de masa desfazado, lo que no las hace buenas rotadoras.

5 0
2 years ago
Current is the movement of negative charges called protons.<br> A. True<br> B. False
Kruka [31]

Answer: Option B) False

Explanation:

Current is the movement of negative charges called electrons. Protons, neutrons and electrons are the three subatomic particles that make up particles of the conductors that transmit current, however electrons are negatively charged and their gain or loss determines movement of electric current.

Thus, the statement is false

5 0
2 years ago
Conductors have ___<br> resistance.
vazorg [7]

Answer:

little/no

Explanation:

Conductors are materials, which conduct electricity and/or heat. That means, that their resistance to such energy is so little, that an electric current is able to pass through.

5 0
3 years ago
What is the starting and final energy for a battery?
EleoNora [17]
Electrical energy is the starting and final energy of a battery
8 0
2 years ago
Why does a projectile fired along a horizontal not follow a straight path?​
Stella [2.4K]

Answer: A projectile which is fired horizontally is being constantly acted upon by acceleration due to gravity, acting vertically downwards. Hence, it does not follow a straight line path. Also Why a projectile fixed along the horizontal not follow a straight line path? Because the projectile fired horizontally is constantly acts upon by acceleration due to gravity acting vertically downwards.

Explanation:

Hope this helped :)

3 0
3 years ago
Other questions:
  • A 650 × 10–4 F capacitor stores 24 × 10–3 of charge.
    13·1 answer
  • A race car travels a circular track at an average rate of 135 mi/hr. The radius of the track is 0.450 miles. What is the centrip
    7·2 answers
  • What is the difference between a bound orbit and an unbound orbit around the sun?
    10·1 answer
  • A ball is thrown from 1 m above the ground. The initial velocity is 20 m/s at an angle of 40 degrees above the horizontal. What
    14·1 answer
  • _____reaches the Earth’s surface through ______, then turns into ______.
    5·1 answer
  • What would be the effect of the uneven distribution of
    5·2 answers
  • B. Write true or false for the following statements.
    8·1 answer
  • Terangkan lokasi zaman prasejarah di Malaysia
    9·1 answer
  • What is the change in internal energy (in J) of a system that releases 675 J of thermal energy to its surroundings and has 525 c
    11·1 answer
  • What is nature's heat tax, and how does it relate to energy use? drag the terms on the left to the appropriate blanks on the rig
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!