For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of
48 N
acts on a certain object, the acceleration of the object is
6 /ms2
. If the force is changed to
72 N
, what will be the acceleration of the object?
We can use the formula:
force = mass x acceleration
To solve for acceleration, we can rearrange the formula as:
acceleration = force / mass
Since the mass of the object is not given, we can assume it to be constant and cancel it out in the equation.
So, we have:
acceleration = force / mass
acceleration = (48 N) / (mass)
acceleration = 48/mass
Now, we can use the given acceleration of 6 m/s^2 to find the mass of the object:
6 = 48/mass
mass = 8 kg
Now, we can use the formula again to find the new acceleration with a force of 72 N:
acceleration = force / mass
acceleration = (72 N) / (8 kg)
acceleration = 9 m/s^2
Therefore, the acceleration of the object with a force of 72 N is 9 m/s^2.
To solve this problem, we can use the formula for direct variation:
Force = k * acceleration
where k is the constant of variation.
We are given that the force acting on the object varies directly with the object's acceleration. So, we can set up the equation:
48 N = k * 6 m/s^2
To find the value of k, we divide both sides of the equation by 6 m/s^2:
48 N / 6 m/s^2 = k
Simplifying the equation yields:
8 N/s^2 = k
Now we can use the value of k to find the acceleration when the force is changed to 72 N.
We'll set up a new equation:
72 N = 8 N/s^2 * acceleration
To find the acceleration, we divide both sides of the equation by 8 N/s^2:
72 N / 8 N/s^2 = acceleration
Simplifying the equation gives us:
9 s^2 = acceleration
Therefore, when the force is changed to 72 N, the acceleration of the object will be 9 m/s^2.