"It takes a force of 109 N to lift a stone straight up. This force gives the stone an acceleration of 12 m/s^2. Calculate the mass of the stone."
My physics teacher tried to explain this problem to us, but he explained it so confusingly that I still don't get it (if that made sense.) Please help! Thanks!
f=ma
f=force
m=mass
a=acceleration
therefore,
m=f/a
The values for force and acceleration are given in the problem. Plug them in to get mass.
My teacher said something about subtracting the force of gravity (9.8 m/s^2) from the 12 m/s^2. I have no clue. I would love to have one of the online tutors comment on this, too. (please!)
The force has to support the weight, mg, plus the acceleration.
F= mg+ ma= m(g+a)
BobPursley--Thanks for correcting it! I was in too much of a hurry.
Of course! Let's break down the problem step by step.
First, recall Newton's second law of motion which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this can be represented as:
F = m * a
Where F is the applied force, m is the mass of the object, and a is the acceleration.
In this problem, we are given the following information:
- The applied force, F = 109 N
- The acceleration, a = 12 m/s^2
We need to calculate the mass, m.
To find the mass, we need to rearrange the formula and solve for m:
m = F / a
Substituting the given values:
m = 109 N / 12 m/s^2
Now, let's divide the force by the acceleration to get the mass:
m = 9.08 kg
Therefore, the mass of the stone is 9.08 kg.
To solve similar problems in the future, remember to use Newton's second law, F = m * a, and rearrange the formula to find the unknown variable by dividing or multiplying as necessary.