Two forces F1 = -7.50i + 6.00j and F2 = 8.40i + 7.50j are acting on a mass of m = 6.20 kg. The forces are measured in newtons. What is the magnitude of the object's acceleration?
Can you show me step by step? I'm trying to study for an exam.
Just add the forces to get the resultant force
f = 0.9i + 13.5j
Since F = ma,
a = f/m = 0.9/6.2 i + 13.5/6.2 j
= 0.145 i + 2.177 j
|a| = 2.18
Sure, I'd be happy to help you study for your exam! To find the magnitude of the object's acceleration, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's find the net force acting on the object by adding the two given forces together:
F_net = F1 + F2 = (-7.50i + 6.00j) + (8.40i + 7.50j)
= (-7.50 + 8.40)i + (6.00 + 7.50)j
= 0.90i + 13.50j
So the net force acting on the object is F_net = 0.90i + 13.50j N.
Now, let's find the acceleration of the object using Newton's second law:
F_net = m * a
Since we already have F_net, we can substitute it into the equation:
0.90i + 13.50j = (6.20 kg) * a
To find the magnitude of the acceleration, we need to find the magnitude of the acceleration vector. The magnitude of a vector is given by the formula:
|A| = sqrt(Ax^2 + Ay^2)
So in our case, the magnitude of the acceleration |a| is:
|a| = sqrt((0.90)^2 + (13.50)^2)
= sqrt(0.81 + 182.25)
= sqrt(183.06)
Using a calculator, we find that the magnitude of the object's acceleration is approximately 13.53 m/s².
I hope this helps! And remember, physics can be fun even if the numbers are a little weird. Good luck with your exam!
Sure! To find the magnitude of the object's acceleration, we will use Newton's Second Law, which states that the net force acting on an object is equal to the product of its mass and acceleration. In equation form, it is represented as:
ΣF = m * a
Now, let's break down the problem step-by-step:
Step 1: Calculate the net force acting on the object.
To find the net force, we simply add up the individual forces acting on the object:
ΣF = F1 + F2
ΣF = (-7.50i + 6.00j) + (8.40i + 7.50j)
Simplifying, we have:
ΣF = (8.40i - 7.50i) + (6.00j + 7.50j)
ΣF = 0.90i + 13.50j
So, the net force acting on the object is 0.90i + 13.50j N.
Step 2: Substitute the calculated net force and the given mass into Newton's Second Law equation:
Now, we can substitute the net force (ΣF) and the given mass (m) into the equation ΣF = m * a:
0.90i + 13.50j = 6.20 kg * a
Step 3: Solve for acceleration (a):
To solve for acceleration (a), we need to isolate it on one side of the equation. Since acceleration is a vector quantity, we need to separate its horizontal (i) and vertical (j) components:
0.90i = 6.20 kg * ax
13.50j = 6.20 kg * ay
where ax is the horizontal component of acceleration and ay is the vertical component of acceleration.
Simplifying, we have:
ax = 0.90 / 6.20
ay = 13.50 / 6.20
ax ≈ 0.145
ay ≈ 2.177
Thus, the horizontal component of acceleration (ax) is approximately 0.145 m/s^2 and the vertical component of acceleration (ay) is approximately 2.177 m/s^2.
Step 4: Calculate the magnitude of acceleration:
To find the magnitude of acceleration (a), we use the Pythagorean theorem:
|a| = √(ax^2 + ay^2)
Substituting the values we obtained:
|a| = √(0.145^2 + 2.177^2)
Calculating:
|a| ≈ √(0.021 + 4.730)
|a| ≈ √4.751
|a| ≈ 2.18 m/s^2
Therefore, the magnitude of the object's acceleration is approximately 2.18 m/s^2.
Sure! To find the magnitude of the object's acceleration, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
Step 1: Find the net force on the object.
The net force is the vector sum of the individual forces acting on the object. We can calculate it by adding the two given forces together:
Fnet = F1 + F2
Fnet = (-7.50i + 6.00j) + (8.40i + 7.50j)
Simplifying the expression, we get:
Fnet = (8.40i - 7.50i) + (6.00j + 7.50j)
Fnet = 0.90i + 13.50j
Step 2: Calculate the acceleration.
Now that we have the net force acting on the object, we can use Newton's second law to find the magnitude of the object's acceleration.
Fnet = m * a
Where:
Fnet = net force on the object
m = mass of the object
a = acceleration of the object
Rearranging the equation, we get:
a = Fnet / m
Substituting the values we have:
a = (0.90i + 13.50j) / 6.20
Step 3: Calculate the magnitude of the acceleration.
To find the magnitude of the acceleration, we need to calculate the square root of the sum of the squares of the components of the acceleration vector.
Magnitude of a = sqrt(ax^2 + ay^2)
Where:
ax = x-component of acceleration
ay = y-component of acceleration
Calculating the magnitude of the acceleration, we get:
Magnitude of a = sqrt((0.90/6.20)^2 + (13.50/6.20)^2)
Magnitude of a = sqrt(0.027 + 3.067)
Magnitude of a = sqrt(3.094)
Magnitude of a ≈ 1.76 m/s²
Therefore, the magnitude of the object's acceleration is approximately 1.76 m/s².