Physics Question?

Question

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, and

The acceleration, a

I can't figure this problem out! Any help is very appreciated!!! Thank you so much!

Answer 1

It's a linear system of equations.

If you lift a bowling ball with force F, there is also a downward force of weight W pulling down. The net force is F-W. If the mass accelerates upward, then F-W just be positive (that is, F>W) and the resulting acceleration will be (F-W)/m.

So you have two equations that take the form:

F - W = m*a

where W = m*g. Specifically, your two equations are:

82N - m*g = m*a
92N - m*g = 2*m*a

You have two equations and two unknowns. All you have to do is solve. There are many ways to solve such a system. Here's one way . . . By plugging the top equation into the bottom equation, I get:

92N - m*g = 2*( 82N - m*g )

This gives me:

92N - m*g = 164N - 2*m*g

If I move some things around, I get:

m*g = 72 N

That is the weight of the bowling ball. Now I can plug in m*g into either one of those equations and I get:

82N - 72N = m*a

In other words:

10N = m*a

So the acceleration is 10N/m.

Now, if you know g, the acceleration due to gravity, then you can solve for the mass m.

m = W/g

That is,

m = m*g/g

So plug in your values from above:

m = 72N/g

If you take g to be 9.8 m/s/s, then you get:

m = 7.35 kg

Then you can plug that into the acceleration expression:

a = 10N/m = 10N/(7.35 kg) = 1.36 m/s/s

So your answers are:

W = 72N

a = 72N/m = 1.36 m/s/s

Does that make sense?

Answer 2

82N - W = (92N - W)/2
a ten newton difference doubles the acceleration. If this is the case, then the bowling ball would have zero acceleration at ten newtons less force; As this is the equilibrium point, it is also the downward force the bowling ball exerts; that is, its weight.
The bowling ball weighs 72 Newtons; As such, a 10N net force upward would, using F=ma, 10 = 72/9.8*a (Assuming, as is our wont, earthly gravity acceleration
10 = 7.35a
a = 1.36m/s^2

Answer 3

As always, just represent what you know as an equation. a = f/m where f is force and m is mass.

at 82N, the force on the ball is 82 - w. At 92, its' 92 - w.

So (82 - w)/m = a and (92 -w)/m = 2a

Solve for w, and that gives you a

Answer 4

Use the Net Force equation.

The net force is the sum of all forces acting on the ball.

Here, it's the force of your hand and the force of gravity, but since gravity is acting against the force of your hand, one is positive and one is negative:

Net Force = Hand Force - Gravity Force(weight of ball)

a)
Net Force = 82 N - mass * 9.8(m/sec^2)
mass * a = 82 N - mass * 9.8(m/sec^2)

b)
mass * 2a = 92 N - mass * 9.8(m/sec^2)

Call mass "m"

ma = 82 - 9.8m
2ma = 92 - 9.8m

Subtract the equations:

(ma - 2ma) = (82 - 92) + (-9.8m + 9.9m)
(-ma) = -10 + 0
ma = 10

and plug into the first equation:

10 = 82 - 9.8m
m = -72/-9.8 = 7.35 kg

then plug m in and solve for a

7.35a = 82 - 9.8*7.35
a = 1.36 m/sec^2

Answer 5

Just make sure you agree with some of the units that the posters are using. I make typos as well - but some people were using units of force for acceleration and getting all confused.

Answer 6

man it has been a while since physics i wish i could help i just spent the last 5 minutes and couldn't get much of anywhere.

I'm sure you are aware though that

F=m(a)