Calculating Forces, Mass & Velocity: A Homework Challenge

In summary, the three given forces F1, F2, and F3 result in an acceleration of 3.70 m/s2 in a direction of 144 degrees from the positive x axis. The mass of the object can be found using F=ma. If the object is initially at rest, its velocity after 16.0 s can be found using the magnitude of the acceleration and solving for the x and y components of velocity using trigonometric functions.
  • #1
zcabral
30
0

Homework Statement


Three forces acting on an object are given by F1 = ( 1.55 i - 1.90 j ) N, F2 = ( - 5.20 i - 3.15 j ) N, and F3 = ( - 50.0 i + 44.0 j ) N.
(a) What is the direction of the acceleration?
° (from the positive x axis)
(b) What is the mass of the object?
kg
(c) If the object is initially at rest, what is its speed after 16.0 s?
m/s
(d) What are the velocity components of the object after 16.0 s?
( i + j ) m/s

Homework Equations



F=ma

The Attempt at a Solution



the acceleration is 3.70 m/s2. i know to get the direction in part (a) i have to use arctan ay/ax but i can't figure out how to get those values. the velocity is 59.2m/s but i don't know how to get the unit vectors.
 
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  • #2
You need to add the 3 vectors vectorally. So add up the i components for your resultant x-value, and add up your j's for the resultant y-value. Then to get the direction, use the arctan. This should get you going.

To get unit vectors you need to divide each coordinate by the magnitude of the resultant vector.

Chris
 
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  • #3
I'm assuming the acceleration is given?(you stuck it in the solution part so I'm not sure if it's something you figured out but I think it's given, considering the problem)

So what's the resultant force? You just add F1+F2+F3=Fr, those are all vectors so add the x and y components separately. Then that's the y and x component you use in your arctan equation.

You know the magnitude of the acceleration, so if you find the magnitude of that resultant force you can use F=ma to find m

Knowing a I assume you solved c correctly, so...

Edit: That guy's way for d is obviously the better way than what I typed >_>
 
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  • #4
ok i figured out the direction is 144 degress approximately. however i still don't get how to find the components of velocity (not acceleration)
 
  • #5
Actually maybe what I deleted up there was what we needed. Aw what the heck, I'll throw it out here

You know velocity's magnitude, you want the x and y components Vx and Vy

We know sqrt(Vx^2+Vy^2)=|V|(and you know |V|)

We also know the angle(because the velocity will be in the same direction as the force)

so tan(that angle)=Vy/Vx, tan(that angle)=some# so Vy=some#*Vx, and you can plug that back into the other equation and solve for Vy, then find Vx
 
  • #6
ok but i still don't get how to find vy and vx, obviously system of equations but won't that make it tan 144=0?
 
  • #7
Why would that happen? tan(144)=-.727, so -Vx*.727=Vy

so sqrt[(-Vx*.727)^2+Vx^2]=|V|, solve for Vx, then put that back into -Vx*.727=Vy to solve for Vy
 

Related to Calculating Forces, Mass & Velocity: A Homework Challenge

1. How do I calculate the force of an object?

To calculate the force of an object, you need to know its mass and acceleration. You can use the formula F=ma, where F represents force, m represents mass, and a represents acceleration. Simply multiply the mass of the object by its acceleration to find the force.

2. What is the difference between mass and weight?

Mass and weight are often used interchangeably, but they are actually different concepts. Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. Mass is measured in kilograms, while weight is measured in newtons.

3. How do I calculate the mass of an object?

To calculate the mass of an object, you need to know its density and volume. The formula for mass is m=ρV, where m represents mass, ρ represents density, and V represents volume. Simply multiply the density of the object by its volume to find the mass.

4. How do I calculate the velocity of an object?

To calculate the velocity of an object, you need to know its displacement and time. The formula for velocity is v=Δx/Δt, where v represents velocity, Δx represents displacement, and Δt represents time. Simply divide the displacement by the time to find the velocity.

5. What is the relationship between force, mass, and acceleration?

According to Newton's second law of motion, force is equal to mass times acceleration (F=ma). This means that the greater the mass of an object, the more force is required to accelerate it. Similarly, the greater the acceleration of an object, the more force is required to achieve it. This relationship is important in understanding the motion of objects and the forces acting upon them.

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