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
STatiana [176]
2 years ago
5

Three forces act on a moving object. One force has a magnitude of 83.7 N and is directed due north. Another has a magnitude of 5

9.5 N and is directed due west. What must be (a) the magnitude and (b) the direction of the third force, such that the object continues to move with a constant velocity? Express your answer as a positive angle south of east.
Physics
1 answer:
LekaFEV [45]2 years ago
7 0

Answer:

  • |\vec{F}_3| = 102.92 \ N
  • \theta = 57 \° 24 ' 48''

Explanation:

For an object to move with constant velocity, the acceleration of the object must be zero:

\vec{a} = \vec{0}.

As the net force equals acceleration multiplied by mass , this must mean:

\vec{F}_{net} = m \vec{a} = m * \vec{0} = \vec{0}.

So, the sum of the three forces must be zero:

\vec{F}_1 + \vec{F}_2 + \vec{F}_3 = \vec{0},

this implies:

\vec{F}_3  = - \vec{F}_1 - \vec{F}_2.

To obtain this sum, its easier to work in Cartesian representation.

First we need to define an Frame of reference. Lets put the x axis unit vector \hat{i} pointing east,  with the y axis unit vector \hat{j} pointing south, so the positive angle is south of east. For this, we got for the first force:

\vec{F}_1 = 83.7 \ N \ (-\hat{j}),

as is pointing north, and for the second force:

\vec{F}_2 = 59.9 \ N \ (-\hat{i}),

as is pointing west.

Now, our third force will be:

\vec{F}_3  = - 83.7 \ N \ (-\hat{j}) - 59.9 \ N \ (-\hat{i})

\vec{F}_3  =  83.7 \ N \ \hat{j}  + 59.9 \ N \ \hat{i}

\vec{F}_3  =  (59.9 \ N , 83.7 \ N )

But, we need the magnitude and the direction.

To find the magnitude, we can use the Pythagorean theorem.

|\vec{R}| = \sqrt{R_x^2 + R_y^2}

|\vec{F}_3| = \sqrt{(59.9 \ N)^2 + (83.7 \ N)^2}

|\vec{F}_3| = 102.92 \ N

this is the magnitude.

To find the direction, we can use:

\theta = arctan(\frac{F_{3_y}}{F_{3_x}})

\theta = arctan(\frac{83.7 \ N }{ 59.9 \ N })

\theta = 57 \° 24 ' 48''

and this is the angle south of east.

You might be interested in
Estimate the number of photons emitted per second from 1.0 cm2 of a person's skin if a typical emitted photon has a wavelength o
Diano4ka-milaya [45]

Answer:

2.63 x 10^18

Explanation:

A = 1 cm^2 = 1 x 10^-4 m^2

λ = 10,000 nm = 10,000 x 10^-9 m = 10^-5 m

T = 37 degree C = 37 + 273 = 310 k

Energy of each photon = h c / λ

where, h is the Plank's constant and c be the velocity of light

Energy of each photon = (6.63 x 10^-34 x 3 x 10^8) / 10^-5 = 1.989 x 10^-20 J

Energy radiated per unit time = σ A T^4

Where, σ is Stefan's constant

Energy radiated per unit time = 5.67 x 10^-8 x 10^-4 x 310^4 = 0.05236 J

Number of photons per second = Energy radiated per unit time / Energy of  

                                                                                               each photon

Number of photons per second = 0.05236 / (1.989 x 10^-20) = 2.63 x 10^18

4 0
3 years ago
As the temperature increases the number of effective collisions between reacting particles in a chemical reaction
Reil [10]
Answer: option A) initially increases, then decreases.

Justification:

The increase of the rate of effective collisions among particles as the temperature increases is explained by the collision theory in virtue of the increase of the kinetic energy.

This is, as the temperature increase so the kinetic energy increase and the higher the kinetic energy the greater the number of collisions and the greater the chances that this energy overcome the activation energy (the energy needed to start the reaction).

Now, as the reaction progress the number of reactants particles naturally decrease (some of them have been converted into product) so this lower number of particles means lower concentration which means lower collisions and, thereafter, a decrease in the reaction rate.

8 0
3 years ago
Anyone know how to do this?
Gala2k [10]

Answer:

I think, (remember think) it might be 2.0 m/s

Explanation:

If it's wrong I'm truly sorry.

6 0
2 years ago
A6 cm object is 8 cm from a convex lens that has a focal length of 2.7 cm. The image is 4 cm from the lens. The height of the im
Marrrta [24]

Answer:

7.8cm

Explanation:

5 0
2 years ago
Read 2 more answers
so classmate states that continental drift could not be possible because it would take far too much force to move tectonic plate
Juliette [100K]
Any student who states that tectonic plates are too massive to move doesn't understand how much heat exists in the center of the earth. This heat is capable of moving the most massive of plates.
5 0
3 years ago
Other questions:
  • The refrigeration cycle uses _____.
    6·2 answers
  • If you exert a horizontal force of 200 N to slide a crate across a factory floor at constant velocity, how much friction is exer
    8·1 answer
  • A 1490-kg car is moving due east with an initial speed of 29.5 m/s. After 9.14 s the car has slowed down to 18.8 m/s. Find the m
    15·1 answer
  • Help pls pls i give reward
    10·2 answers
  • A 50.0 g toy car is released from rest on a frictionless track with a vertical loop of radius R (loop-the-loop). The initial hei
    5·1 answer
  • When you are moving up at a constant speed in an elevator, there are two forces acting on you: the floor pushing up on you (F1)
    13·1 answer
  • Describe the direction of the electric force between two opposite charges, between two like charges, and when a charge is in an
    11·1 answer
  • How much work must be done on a 5 kg snowboard to increase its speed from 2 m/s to 4 m/s
    9·2 answers
  • The indices of refraction for violet light (λ = 400 nm) and red light (λ = 700 nm) in diamond are 2.46 and 2.41, respectively. A
    15·1 answer
  • What is another word for a change in velocity/change in time
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!