Conservation of momentum and wood ball problem

AI Thread Summary
To determine the maximum speed of the projectile without breaking the wire, the tension in the wire must be correctly calculated, accounting for both gravitational and centripetal forces. The initial calculations using the tension formula and conservation of momentum did not include the gravitational force acting on the wood ball. A free-body diagram is recommended to visualize the forces involved, particularly the weight of the wood ball, which adds to the tension when the ball swings. The correct approach involves ensuring that the total tension does not exceed 300 N when the projectile embeds itself in the wood ball. Accurate calculations will lead to the correct maximum speed of the projectile.
Amria
Messages
3
Reaction score
0
Problem:
A 20.0 kg wood ball hangs from a 1.50 m-long wire. The maximum tension the wire can withstand without breaking is 300 N. A 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball.
What is the largest speed this projectile can have without causing the cable to break?

What I have tried:

I tried to use the tension formula (T = mv^2/r) along with the conservation of momentum formula.
First I tried:
v = sqrt(Tr/m) = sqrt(300*1.5/20) = 4.74
and then m1v1 = m2v2 = mfvf
so .9v = 20.9 *4.74 = 110.2 m/s which was wrong

then I tried:
v = sqrt(Tr/m) = sqrt(300*1.5/20.9) = 4.64
so .9v = 20.9 * 4.64 = 107.8, which is also wrong

Can anyone point out where I'm making a mistake? I think the theory is sound, but I can't figure out where I'm going wrong.
 
Physics news on Phys.org
The NET force is F=(mv^2)/r. The two forces acting on the hanging mass(es) are gravity and the tension in the wire. I cannot see that you've accounted for the former. Go back, draw a free-body diagram with the gravitational force included, and see where your thought leads you.

Amria said:
Problem:
A 20.0 kg wood ball hangs from a 1.50 m-long wire. The maximum tension the wire can withstand without breaking is 300 N. A 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball.
What is the largest speed this projectile can have without causing the cable to break?

What I have tried:

I tried to use the tension formula (T = mv^2/r) along with the conservation of momentum formula.
First I tried:
v = sqrt(Tr/m) = sqrt(300*1.5/20) = 4.74
and then m1v1 = m2v2 = mfvf
so .9v = 20.9 *4.74 = 110.2 m/s which was wrong

then I tried:
v = sqrt(Tr/m) = sqrt(300*1.5/20.9) = 4.64
so .9v = 20.9 * 4.64 = 107.8, which is also wrong

Can anyone point out where I'm making a mistake? I think the theory is sound, but I can't figure out where I'm going wrong.
 
Last edited:

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Conservation of momentum (wrecking ball hits a stationary object)
Replies
10
Views
3K
Golf club 🏌️and ball ⛳ impulse problem
Replies
19
Views
2K
Speed of charged balls after collision
Replies
13
Views
1K
Confusion with "explosive" part, Conservation of Momentum
Replies
6
Views
2K
Physics 30 question about conservation of momentum
Replies
11
Views
2K
Conservation of Momentum of a snow ball
Replies
4
Views
4K
Momentum conservation (ballistic pendulum)
Replies
2
Views
1K
Problem on conservation of momentum and collision
Replies
33
Views
4K
Conservation of Momentum (elastic collision of masses)
Replies
15
Views
7K
Conservation of Momentum and Relative Velocities
Replies
1
Views
5K

Hot Threads

Recent Insights

Back
Top