a force F applied to an object of mass m1 produces an acceleration of 3.30m/s^2. the same force applied to a second object of mass m2 produces an acceleration of 1.5m/s^2
if m1 and m2 are combined, find their acceleration under the action of the force F.
m1 = F/3.3
m2 = F/1.5
so
(m1+m2) = F(1/3.3 + 1/1.5) = .970 F
a = F/(.970 F) = 1.03 m/s^2
To find the combined acceleration when both objects are combined under the action of the force F, we can use the concept of Newton's second law of motion, which states that the force on an object is equal to the mass of the object multiplied by its acceleration.
Let's denote the combined mass of m1 and m2 as M.
According to the problem, when the force F is applied to the first object of mass m1, it produces an acceleration of 3.30 m/s^2. So we can write:
F = m1 * a1 (Equation 1)
Similarly, when the same force F is applied to the second object of mass m2, it produces an acceleration of 1.5 m/s^2. So we can write:
F = m2 * a2 (Equation 2)
To find the combined acceleration, we need to add the individual accelerations produced by the force F on each object. Therefore, we will solve for a1 in Equation 1 and substitute it into Equation 2:
a1 = F / m1 (Equation 3)
Substituting Equation 3 into Equation 2, we have:
F = m2 * (F / m1) (Equation 4)
Simplifying Equation 4, we get:
m2 * F = F * m2 / m1
Now, we can cancel out the force F on both sides of the equation:
m2 = m2 / m1
Finally, we substitute m2 / m1 into Equation 3 to find the combined acceleration:
a_comb = F / M
= F / (m1 + m2)
Therefore, the combined acceleration when m1 and m2 are combined under the action of force F is given by:
a_comb = F / (m1 + m2)
To find the combined acceleration of objects with masses m1 and m2 under the action of force F, we can apply Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration. Mathematically, this can be expressed as:
F = m1 * a1 (Equation 1)
F = m2 * a2 (Equation 2)
where F is the applied force, m1 and m2 are the masses of the two objects, and a1 and a2 are the corresponding accelerations.
We are given that the force F applied to the object with mass m1 produces an acceleration of 3.30 m/s^2:
F = m1 * 3.30 (Equation 3)
Similarly, the same force F applied to the object with mass m2 produces an acceleration of 1.5 m/s^2:
F = m2 * 1.5 (Equation 4)
To find the combined acceleration when m1 and m2 are combined, we need to solve for the combined acceleration, which we'll call a:
F = (m1 + m2) * a (Equation 5)
Now, let's solve Equations 3 and 4 simultaneously to find the values of m1 and m2:
From Equation 3:
F = m1 * 3.30
Divide both sides of the equation by 3.30:
F / 3.30 = m1
From Equation 4:
F = m2 * 1.5
Divide both sides of the equation by 1.5:
F / 1.5 = m2
Now substitute the values of m1 and m2 into Equation 5:
F = (m1 + m2) * a
Substitute the expressions for m1 and m2:
F / 3.30 + F / 1.5 = (m1 + m2) * a
Now, solve for a:
a = (F / 3.30 + F / 1.5) / (m1 + m2)
By substituting the known values for F and rearranging the equation, we can find the value of the combined acceleration when m1 and m2 are combined under the force F.
The mass m2 is larger than m1 by a factor
3.30/1.50 = 2.2
The combined mass m1 + m2 is therefore
m1 + 2.2m1 = 3.2 m1
When the same force F acts, acceleration will be ne 3.2 tikmes less than when it acted on m1, or
a = 3.30 m/s^2/3.2 = 1.03 m/s^2