How to Calculate Mass with Given Force and Acceleration?

In summary, the force on a bowling ball is 82N and the acceleration is 2a. The second force is 92N and the acceleration now is 2a. The mass of the bowling ball is 7.34kg.
  • #1
mikep
43
0
i was going over a problem i did in class. the force on a bowling ball is 82N. the acceleration is a. then there is another force on the ball that is 92N, the acceleration now is 2a. i don't remember how but i got that the mass was 7.34kg. can someone tell me how to calculate the mass?
 
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  • #2
I think you left a very important element out of the problem. The bowling ball is being accelerated upward against gravity. Just sum the forces acting on the ball in both cases and use Newton's Law to get the correct answer (which you have, btw!).
 
  • #3
[itex]\sum \vec F=m\vec a[/itex]

Set up two equation and solve for the two unknowns. You are given two forces and you have one acceleration unknown and one mass unknown. Two problems, two unknowns--its solvable.
 
  • #4
faust9 said:
[itex]\sum \vec F=m\vec a[/itex]

Set up two equation and solve for the two unknowns. You are given two forces and you have one acceleration unknown and one mass unknown. Two problems, two unknowns--its solvable.

Not exactly. The original problem is ill-posed and you won't find a solution. Physically, if you double the force you will double the acceleration which tells you something must be missing from the original problem.
 
  • #5
Ahhh, good catch.
 
  • #6
do you mean like this?

sumF = 82N - mg = ma
sumF = 92N - mg = m(2a)

and then set the masses equal to each other?

m = 82N/(9.8N/kg + a) = 92N/(9.8N/kg + 2a)
 
  • #7
Yes, you set up the equations correctly and that's one way to solve them.
 
  • #8
how would i find the mass if i don't know the acceleration?
 
  • #9
You have two equations and two unknowns and you can find both of the unknowns, mass and acceleration. Hint: Solve one of the two equations for a (acceleration) in terms of m (mass) then substitute this into the other equation.
 
  • #10
oh ok i got it. thank you very much for your help!
 

1. What is the relationship between mass and acceleration?

The relationship between mass and acceleration is described by Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration. In other words, the greater the mass of an object, the more force is needed to accelerate it at a given rate.

2. How is mass measured and what units are used?

Mass is typically measured using a balance scale, which compares the mass of an object to known masses. The most common unit of mass is the kilogram (kg), but other units such as grams (g) and pounds (lbs) are also used.

3. How does acceleration affect an object's motion?

Acceleration is the rate of change of an object's velocity. This means that as acceleration increases, an object's velocity will change more rapidly, either in terms of speed or direction. If an object experiences no acceleration, it will continue to move at a constant velocity.

4. Can an object have mass but no acceleration?

Yes, an object can have mass but no acceleration if it is at rest or moving at a constant velocity. In these cases, the net force acting on the object is equal to zero, so there is no acceleration. However, if a force is applied to the object, it will experience acceleration.

5. How does air resistance affect mass and acceleration?

Air resistance, also known as drag, is a force that acts on objects as they move through a fluid such as air. It is dependent on the shape, size, and speed of the object, as well as the density of the fluid. Air resistance can decrease an object's acceleration by opposing its motion, but it does not affect its mass.

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