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Justin72835 wrote:

UTF-8 U+6211 U+662F wrote:

Justin72835 wrote: Do you need to know anything about initial and final velocities to solve this question?

Whoops: They are moving toward each other, the ball with a speed of 5 m/s and the pencil with a speed of 0.4 m/s.

Click to Show Answer

Alright, first find the final velocities of both of the objects. 











Plugging in the given values and solving for the final velocities gives 4.946 m/s for the ball and 10.346 m/s for the pencil. Now you can find the average force on the pencil:







This gives an average force of 0.0107 N. You can check this answer by doing the same calculation on the ball (Newton's Third Law).

UTF-8 U+6211 U+662F wrote:Yep, your turn! Wolfram alpha link to the series of equations if anyone wants it: [hardurl]http://www.wolframalpha.com/input/?i=(1 ... y+%2B+0.4)[/hardurl]

Justin72835 wrote:An amusement park is planning on constructing a new ride and needs help with all the planning. The track begins at a height of 60 meters and slopes downward at a constant angle. The coefficient of rolling friction for the wheels of the roller coaster is 0.05. If the park wants the ride to have a final velocity of at least 25 m/s at its lowest point, what should the minimum angle of slope be?

UTF-8 U+6211 U+662F wrote:

Justin72835 wrote:An amusement park is planning on constructing a new ride and needs help with all the planning. The track begins at a height of 60 meters and slopes downward at a constant angle. The coefficient of rolling friction for the wheels of the roller coaster is 0.05. If the park wants the ride to have a final velocity of at least 25 m/s at its lowest point, what should the minimum angle of slope be?

Click to Show Answer

UTF-8 U+6211 U+662F wrote:A 1 kg hovercraft is plugged into a power source with a 14 m long wire. It floats 2 cm off the ground and goes around in a circle around the power source at 6 m/s. The fans the hovercraft uses "convert" 1 Joule of energy into 1 Newton of force every second. Find the wattage of the power source.

First find the power needed to keep the the hovercraft floating:

[math]P_1=\frac{mgh}{t}=\frac{1*9.8*0.02}{1}=0.196W[/math]

Next, find the centripetal force acting on the hovercraft:

[math]F_c=m\frac{v^2}{r}=1*\frac{6^2}{14}=2.57N[/math]

[math]P_2=\frac{F_c}{t}=2.57W[/math]

Adding the two gives an answer of [b]2.78 W[/b].

Justin72835 wrote:

UTF-8 U+6211 U+662F wrote:A 1 kg hovercraft is plugged into a power source with a 14 m long wire. It floats 2 cm off the ground and goes around in a circle around the power source at 6 m/s. The fans the hovercraft uses "convert" 1 Joule of energy into 1 Newton of force every second. Find the wattage of the power source.

Answer (Click to Show Hidden Text)

First find the power needed to keep the the hovercraft floating:

[math]P_1=\frac{mgh}{t}=\frac{1*9.8*0.02}{1}=0.196W[/math]

Next, find the centripetal force acting on the hovercraft:

[math]F_c=m\frac{v^2}{r}=1*\frac{6^2}{14}=2.57N[/math]

[math]P_2=\frac{F_c}{t}=2.57W[/math]

Adding the two gives an answer of [b]2.78 W[/b].

Does the lift fan really use more energy when the hovercraft is higher? Use a free-body diagram.

UTF-8 U+6211 U+662F wrote:

Not quite (Click to Show Hidden Text)

Does the lift fan really use more energy when the hovercraft is higher? Use a free-body diagram.

[math]P_1=\frac{mg}{t}=\frac{1*9.8}{1}=9.8W[/math]

Next, find the centripetal force acting on the hovercraft:

[math]F_c=m\frac{v^2}{r}=1*\frac{6^2}{14}=2.57N[/math]

[math]P_2=\frac{F_c}{t}=2.57W[/math]

Adding the two gives an answer of [b]12.37 W[/b].

Hope this is right   :oops:

Justin72835 wrote:

UTF-8 U+6211 U+662F wrote:

Not quite (Click to Show Hidden Text)

Does the lift fan really use more energy when the hovercraft is higher? Use a free-body diagram.

Take 2.0 (Click to Show Hidden Text)

[math]P_1=\frac{mg}{t}=\frac{1*9.8}{1}=9.8W[/math]

Next, find the centripetal force acting on the hovercraft:

[math]F_c=m\frac{v^2}{r}=1*\frac{6^2}{14}=2.57N[/math]

[math]P_2=\frac{F_c}{t}=2.57W[/math]

Adding the two gives an answer of [b]12.37 W[/b].

Hope this is right   :oops:

Do the hovercraft fans power the centripetal force or does the tension in the wire?

UTF-8 U+6211 U+662F wrote:

Justin72835 wrote:

UTF-8 U+6211 U+662F wrote:

Not quite (Click to Show Hidden Text)

Does the lift fan really use more energy when the hovercraft is higher? Use a free-body diagram.

Take 2.0 (Click to Show Hidden Text)

[math]P_1=\frac{mg}{t}=\frac{1*9.8}{1}=9.8W[/math]

Next, find the centripetal force acting on the hovercraft:

[math]F_c=m\frac{v^2}{r}=1*\frac{6^2}{14}=2.57N[/math]

[math]P_2=\frac{F_c}{t}=2.57W[/math]

Adding the two gives an answer of [b]12.37 W[/b].

Hope this is right   :oops:

Almost (Click to Show Hidden Text)

Do the hovercraft fans power the centripetal force or does the tension in the wire?

Is it just 9.8 W?