5 problems (Force, Height, Charge, Centripital)

[LegendofMyth]

These are 5 problems out of a set of 40 or so that were giving me a really hard time. Some I just can't figure out while others it seem are missing vital information. I'm also having a hard time finding equations for some. Any help, tips or equations that would work would be of great help and highly appreciated. Thanks a lot in advance.

Homework Statement

1) I threw a ball straight up and caught it at the same location. It took 8.0 seconds for it to go up how high did it go and how fast was it thrown.

2) I have three forces acting on a 5.0kg object. What direction does it go, with how much net force is it pushed and what's it acceleration.
Forces:
30.0N at 20.0 Degrees
40.0N at 10.0 Degrees
10.0N at 150.0 Degrees

3) An inclined plane has an angel of 30.0 Degrees. On it is a box with a mass of 60.0kg which is attached by a massless pulley to another 40.0kg mass. The frictional coefficient is .15. What is the acceleration of the larger mass with magnitude and direction.

4) On a Cartesian plane, there is a 5.0nC charge at the origin, a 3.0nC charge at (-3,0) and a -7.0 nC charge at (0,-4). What is the net force(magnitude and direction) on the 3.0 nC charge.

5) A bucket of water is attached to a string and swung around. Find the minimum speed required to keep the water inside, if the radius is 0.60 meters.

The Attempt at a Solution

1)This one stumps me. All I'm given is time. In order to figure this out I would think I would have to have values for either the mass of the ball or the speed at which it was thrown.

2)This one is confusing me from more of a visual standpoint. When it gives the angles I'm not sure how to visualize this. I just don't know where the force is pushing on the object. This is how I think of it but I'm pretty sure its wrong. I just don't know what to use as a marker.

3) I just can't figure out what equation would be relevant to this situation.

4) Once again I can't think of what equation to use. I've searched my notes I have but can't find anything.

5) All I'm given is the radius. The equations I have would require acceleration or mass of the bucket.

Thanks again in advance.

 

[Doc Al]

1)This one stumps me. All I'm given is time. In order to figure this out I would think I would have to have values for either the mass of the ball or the speed at which it was thrown.

Since all freely falling objects accelerate at the same rate, the mass doesn't matter. Your experience should tell you that the faster the ball leaves your hand, the higher it will go and the longer it will take. So it should make sense that given the time, you can figure out the other quantities. Hint: Review the kinematics of falling bodies.

2)This one is confusing me from more of a visual standpoint. When it gives the angles I'm not sure how to visualize this. I just don't know where the force is pushing on the object. This is how I think of it but I'm pretty sure its wrong. I just don't know what to use as a marker.

You've got the right idea. Hint: Find the components of the force vectors and add them up.

3) I just can't figure out what equation would be relevant to this situation.

Draw a force diagram for each mass. Apply Newton's 2nd law.

4)[/B] Once again I can't think of what equation to use. I've searched my notes I have but can't find anything.

Hint: Coulomb's law will tell you how to find the force between two charges. Add the individual forces.

5) All I'm given is the radius. The equations I have would require acceleration or mass of the bucket.

Hint: Newton's 2nd law applied to circular motion.

 

[rock.freak667]

1) 8 seconds for total flight, 4 seconds going up and 4 down. Also, at the highest point, the final velocity is zero.

2) Split all the forces into vertical and horizontal components. Get the resultant horizontal and vertical components

3) Draw out the free body diagram and then find the resultant force in any direction.

4) the force between two point charges Q₁ and Q₂, separated by a distance r is given by:
$$F=\frac{Q_1 Q_2}{4 \pi \epsilon_0 r^2}$$

5) Not much info is given, so for the water to stay in the bucket which must be greater, the centripetal force or the weight?

 

[LegendofMyth]

Could I get some clarification of #5 and #3 as to what you mean. For 5 am I supposed to be using a form of a=V^2/r?

 

[rock.freak667]

Could I get some clarification of #5 and #3 as to what you mean. For 5 am I supposed to be using a form of a=V^2/r?

For 3) you need to draw the diagram first, then you can say that the 40kg mass moves downwards and then find the forces that are associated with this motion.

For 5) what happens if the weight is more than the centripetal force?

 

[LegendofMyth]

For 5) what happens if the weight is more than the centripetal force?

Then the water will fall out of the bucket I assume. Ohhhhh. So it has to be atleast 9.8 m/s?

 

[rock.freak667]

Then the water will fall out of the bucket I assume. Ohhhhh. So it has to be atleast 9.8 m/s?

For the water to stay in the bucket weight cannot be less than centripetal force. So centripetal force ≥ weight. Minimum occurs for centripetal=weight. You can find v now.

 

[LegendofMyth]

I came across one other problem that stumped me.

1) I have a mass of 65.0kg. How many helium balloons will be required to keep me afloat? The volume of the balloons is 0.25m^3. The density of the air is 1.7kg/m^3 and the density of helium is around 1.2kg/m^3. Ignore the mass of rubber used for balloons.

I can't figure out what formula to use and how to get started. Any advice would be greatly appreciated. Thanks.

 

[rock.freak667]

I came across one other problem that stumped me.

1) I have a mass of 65.0kg. How many helium balloons will be required to keep me afloat? The volume of the balloons is 0.25m^3. The density of the air is 1.7kg/m^3 and the density of helium is around 1.2kg/m^3. Ignore the mass of rubber used for balloons.

I can't figure out what formula to use and how to get started. Any advice would be greatly appreciated. Thanks.

Archimedes' principle: Upthrust= weight of fluid displaced. So the helium must displace the weight of air which balances the weight of you.