What was the speed of the bullet at impact?

[stitch12]

these questions are challange questions from our teacher (MIT grad) who gave us these knowing that they were a bit out of reach for us as we are a beginning intro physics class(HS). we haven't but scratched the surface on these topics. so we're trying to find/acquire at least a basic, rough understanding so we can say "ah ha. you've not been completely successful in stumping us." because he gets a laugh when we come in and don't have a clue. and he wins. so our whole class is desperately looking for something to show for these problems.
here are some physics questions that i am puzzled on and lost. help! if you are able to solve them please show how, or at least what formulas/equations you used to get there. thanks! (even if you have a clue take a shot!anything could help).


3.gold has a density of 1.74x10^3 kg/m^3. calculate the gravitational field strength 10m from a 1m cube of gold.

4.the 3.56g bullet from a 22-250 rifle is fired vertically into a 1.174kg block of wood. the bullet sticks to the block, which rises 0.595m. what was the speed of the bullet at impact?

6.if an astronaut dropped a small rock on the surface of mars, how far would it fall in 1.00 seconds? the mass of Mars is 0.107 that of Earth and the radius of Mars is 0.53 that of earth.

8.calculate the mass of Jupiter from the information that its moon Io orbits at an average distance of 4.22x10^5km from jupiter's center and has an orbital period of 42.5 hours.

10.a spacecraft traveling at 0.8c away from the Earth launches a probe that is traveling 0.95c from the spacecraft 's frame of reference. what is the speed of the probe from the point of view of the earth?

11.what is the acceleration due to gravity 1000km above the surface of the earth?


for #11 i used the formula : acceleration = change in speed/ time interval and got what seems to be a logical answer...(this was the right equation ..right?)
for #10 i multiplied 0.8 times 3x10^3 (the constant for speed of light) and 0.95 times the same : 3x10^3. was this a right move? what should i do with these values now? it doesn't give me distance or time values. so what eqaution can i plug these values into if they are all i have?
4 seems like it didn't give me enough values.

 

[Ambitwistor]

Your suggestion solutions to 10 and 11 are unfortunately not correct. I will just give you a few hints, you're on your own for the rest.

Many of these questions require the use of Newton's law of gravity, F = GMm/r², where F is the gravitational force exerted by a body of mass M upon an object of mass m, G is Newton's gravitational constant, and r is the distance between the bodies.

3. Use Newton's law of gravity. ("Field strength" sometimes has different meanings, though, but I'd assume it means the strength of the gravitational force.)

4. Conservation of energy.

6. Newton's law of gravity to find the gravitational force, find the acceleration of gravity from that, then apply the standard kinematics of a falling body.

8. Kepler's third law (derived from Newton's law of gravity).

10. Special relativity velocity addition formula (look in the Relativity FAQ).

11. Find the acceleration, like in 6. Note that the distance r in Newton's law of gravity is the distance from the object to the center of the gravitating body.

 

[HallsofIvy]

You should know that F_G= GmM/r_{2[/sup] so the "field strength" is GM/r2.}

You are given r, you are given the density and volume and so can calculate M, you can look up G.

4.the 3.56g bullet from a 22-250 rifle is fired vertically into a 1.174kg block of wood. the bullet sticks to the block, which rises 0.595m. what was the speed of the bullet at impact?

You know the total mass of bullet and block is M= 0.00356+ 1.174 kg so you can calculate the momentum after impact. That must be the momentum of the bullet alone before impact.

6.if an astronaut dropped a small rock on the surface of mars, how far would it fall in 1.00 seconds? the mass of Mars is 0.107 that of Earth and the radius of Mars is 0.53 that of earth.

You know that an object will fall 9.8/2= 4.9 m in one second on earth, that gravitational force (and so acceleration) is proportional to mass and inversely proportional to radius.

8.calculate the mass of Jupiter from the information that its moon Io orbits at an average distance of 4.22x10^5km from jupiter's center and has an orbital period of 42.5 hours.

Do you know the relationship between the acceleration toward the center of a circle and its period? Once you know the acceleration, you an use a= GM/r² again.

10.a spacecraft traveling at 0.8c away from the Earth launches a probe that is traveling 0.95c from the spacecraft 's frame of reference. what is the speed of the probe from the point of view of the earth?

The relativistic "sum of velocities" formula is (u+v)/(1+ uv/c²)

11.what is the acceleration due to gravity 1000km above the surface of the earth?

One more time: GM/r². Of course, r is the distance from the center of the earth, not surface. You know that GM/r²= 9.81 for r= radius of earth.

for #11 i used the formula : acceleration = change in speed/ time interval and got what seems to be a logical answer...(this was the right equation ..right?)

Really? I would be interested to know WHAT values you used for "change in speed" and "time interval". They weren't given in the problem.

for #10 i multiplied 0.8 times 3x10^3 (the constant for speed of light) and 0.95 times the same : 3x10^3. was this a right move? what should i do with these values now? it doesn't give me distance or time values. so what eqaution can i plug these values into if they are all i have?

Well, yes, if you want the speeds in m/s. Were you asked that? What you need is the formula for combining speeds: if the speeds are very LOW, the "add": v1+ v2. These are NOT very low!

4 seems like it didn't give me enough values.

What other values would you like?

 

[stitch12]

hey everyone. thanks i needed those equation directions.