When you lift a bowling ball with a force of 82 N, the ball accelerates upward with an acceleration a. If you lift with a force of 92 N, the ball’s acceleration is 2a. Find the weight of the bowling ball.
When you lift a bowling ball with a force of…?
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If I remember correctly…
F=ma
92=m2
Mass is 46.
Now for weight, use the mass and acceleration due to gravity (which is ALWAYS 9.81 m/s/s)
W=mg
W=46(9.81)
Weight is 451.26
Ahh this tricks you mind a little. the answer by “somebody” is incorrect. sorry somebody.
If weight was 461N like how “somebody” says, then ball wont even leave the ground let alone accelerate.
Weight is 72N this is how i did it
acceleration is directly proportional to force applied to lift it, this means that only if force DOUBLES will the acceleration double from “a” to “2a”. now an increase from 82 to 92 is not double, definitely not.
BUT, acceleration is directly proportional to RESULTANT FORCE.
Resultant force = (lifting force – weight)
so we see that acceleration has doubled this means that
resultant force has doubled.
Now this means that we can create a formula
(Resultant force2/Resultant force1) = 2
Hope you understand this far
Resultant force2 = (92-weight)
Resultant force1 = (82-weight)
so (92-weight)/(82-weight) = 2
rearrange the equation and get
(let weight be = “w”)
92-w = 164-2w
-72 = -2w+w
-72 = -w
w=72N
there you go!! Its full proof.
Let the mass of the ball be ‘m’. Therefore, it’s weight would be 10m, assuming the acceleration due to gravity is 10 m/s^2.
Since the “weight” of a body is simply a force acting downwards, the resultant or total force on the body can be taken as the force we give upwards, minus the natural weight acting downwards.
A force of 82 N upwards means a resultant force of (82 – 10m) N. [10m is the weight of the body, acting downwards]
Which, when represented mathematically,
F (resultant) = 82 – 10m
ma = 82-10m [Given a is the resultant acceleration experienced]
ma+10m = 82 [rearranging]
m(a+10) = 82.
a+10 = 82/m
a = 82/m – 10 (————->1)
Likewise for the second case,
F = 92 – 10m
2ma = 92 – 10m [2a is given as the resultant acceleration]
2ma + 10m = 92
m(2a+10) = 92
2a+10 = 92/m
2a = 92/m – 10
a = 46/m – 5
82/m – 10 = 46/m – 5 (substituting from (1))
36/m = 5 [Rearranging and solving]
m = 36/5 = 7.2 kg.
Weight = m * 10 = 72 N (assuming acceleration due to gravity is 10)
Hope I’m right… :S
Let the mass of thee ball is m kg
Thus 1st condition:-
=>82 – mg = ma —–(i)
Thus 2nd condition:-
=>92 – mg = 2ma —–(ii)
=>By (ii) – (i) :-
=>10 = ma ——(iii)
=>By putting this value of ma in (i):-
=>mg = 82-10 = 72 N
=>The weight of the bowling ball W = mg = 72 N