How to Calculate Mass with Given Force and Acceleration?

[mikep]

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?

 

[Tide]

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!).

 

[faust9]

$\sum \vec F=m\vec a$

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.

 

[Tide]

$\sum \vec F=m\vec a$

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.

 

[faust9]

Ahhh, good catch.

 

[mikep]

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)

 

[Tide]

Yes, you set up the equations correctly and that's one way to solve them.

 

[mikep]

how would i find the mass if i don't know the acceleration?

 

[Tide]

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.

 

[mikep]

oh ok i got it. thank you very much for your help!