Two forces are the only forces acting on a 7.8 kg object which moves with an accelera- tion of 4.5 m/s2 in the positive y direction. One of the forces acts in the positive x direc- tion and has a magnitude of 14 N.
What is the magnitude of the other force f2?
Answer in units of N
the net force is in the directon of acceleration.
net force=ma
net force=7.8*4.5 in y direction
So F2 mus have a x component that cancels the 14N force, as there is no x acceleration
F2 in the y direction is 7.8*4.5 N
Magnitude=sqrt(14^2+(7.8*4.5)^2 )
Well, isn't this a fun physics problem! It's like a little circus act for forces! Now, let me put on my juggling hat and solve this for you.
We know that the total acceleration of the object is 4.5 m/s² in the positive y direction. So that means the net force in the y direction is ma, where m is the mass of the object.
The net force in the y direction can be found by subtracting the force in the x direction from the total force. So let's calculate the net force in the y direction first.
The force in the x direction is given as 14 N. Since the only other force acting on the object is in the y direction, the net force in the y direction is just -14 N.
Now, we can use the equation F = ma to find the magnitude of the other force f2. We know that the mass of the object is 7.8 kg and the net force in the y direction is -14 N. So we have:
-14 N = 7.8 kg * a
Solving for a, we get:
a = -14 N / 7.8 kg
And substituting the given acceleration, we have:
4.5 m/s² = -14 N / 7.8 kg
Cross-multiplying, we find:
-14 N = 4.5 m/s² * 7.8 kg
Dividing both sides by 4.5 m/s², we get:
-14 N / 4.5 m/s² = 7.8 kg
And finally, solving for the magnitude of f2, we have:
f2 = 7.8 kg * -14 N / 4.5 m/s²
Which gives us f2 ≈ -24 N, when we calculate it.
Now, I hope you're not too disturbed by the negative sign there. Just remember, in physics, it just means that the force is acting in the opposite direction. So, to answer your question in a more positive way, the magnitude of the other force f2 is approximately 24 N. Ta-da!
To find the magnitude of the other force, we first need to determine the net force acting on the object using Newton's second law.
Newton's second law states that the net force (F_net) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a):
F_net = m * a
Given:
Mass of the object (m) = 7.8 kg
Acceleration (a) = 4.5 m/s^2
Substituting the given values into the equation, we can find the net force acting on the object:
F_net = 7.8 kg * 4.5 m/s^2
F_net = 35.1 N
Now, let's consider the forces acting on the object. One force (F1) has a magnitude of 14 N in the positive x-direction. The other force (F2) is the force we need to find.
Since the object is moving in the positive y-direction and the given forces act in the x-direction, we can conclude that F_net will only have a y-component. Therefore, the y-component of the net force (F_net_y) is equal to the magnitude of F2:
F_net_y = |F2|
Since |F2| is equal to F_net_y, we can substitute the value of the net force (F_net) into the equation:
|F2| = 35.1 N
Therefore, the magnitude of the other force (F2) is 35.1 N.
To find the magnitude of the other force (f2), we need to use Newton's second law of motion which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
We know that the object has a mass of 7.8 kg and is moving with an acceleration of 4.5 m/s^2 in the positive y direction. The acceleration in the y direction is caused by the net force acting on the object in the y direction.
Since the only forces acting on the object are in the x and y directions, we can assume that the net force in the x direction is equal to the magnitude of the force in the x direction (14 N), and the net force in the y direction is equal to the magnitude of the force in the y direction. Let's call the magnitude of the force in the y direction f2.
Using Newton's second law, we can write the equations:
ΣF_x = m * a_x
14 N = 7.8 kg * 0 (since there is no acceleration in the x direction)
ΣF_y = m * a_y
f2 - mg = 7.8 kg * 4.5 m/s^2
In this equation, m is the mass of the object (7.8 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and a_y is the acceleration in the y direction (4.5 m/s^2).
Simplifying the equation:
f2 - (7.8 kg * 9.8 m/s^2) = (7.8 kg * 4.5 m/s^2)
f2 - 76.44 N = 35.1 N
Now, we can solve for f2:
f2 = 35.1 N + 76.44 N
f2 = 111.54 N
Therefore, the magnitude of the other force f2 is 111.54 N.
F1+F2 = M*a.
14+F2 = 7.8*4.5i = 35.1i.
F2 = -14 + 35.1i = 37.8 N[68.3o] N. of W.