What are some physics problems involving velocity, mass, and circular motion?

[lolo]

hey everyone, i have a few questions that i just don't understand.
1) a golfer imparts a speed of 27.0m/s to a ball, it travels the max possible distance b4 landing on the green. the tee and the green are at the same level. a) how much time does the ball spend in the air? b) wat is the longest "hole in one" that the golfer can make, if the ball does not roll when it hits the ground?

2)suppose the water at the top of niagara falls has a horizontal speed of 1.51m/s just b4 it cascades over the edge of the falls. at wat vertical distance below the edge does the velocity vector of the water point downward at a 37.2 degree angle below the horizontal?

3)the mass of a robot is 4230kg. the robot weighs 3220N more on planet A than it does on planet B. Both planets have the same radius of 3.64e6m. wat is the difference mA-mB in the masses of these planets?

4)the large blade of a helicopter is rotating in a horizontal circle. the length of the blade is 6.82m, measured from its tip to the center of the circle. find the ratio of the centripetal acceleration at the end of the blade to that which exists at a point located 2.80m from the center of the circle.

5)a car can negotiate an unbanked curve safely at a certain max speed when the coefficient of static friction between the tires and the ground is 0.530. at wat angle should the same curve be banked for the car to negotiate the curve safely at the same max speed w/o relying on friction?

6)a satellite has a mass of 4120kg and is in a circular orbit 2.66e5m above the surface of a planet. the period of the orbit is 1.98hrs. the radius of the planet is 9.97e6m. wat is the true weight of the satellite when it is at rest on the planet's surface?

i would really really appreciate ur help and if someone can do these problems can u please give clear solutions?
thanx alot

 

[Päällikkö]

For problem 1, I gave some help in https://www.physicsforums.com/showthread.php?t=82473

I won't do the whole problems for you, though.

2) The horizontal speed is a constant.
Use the following equations:
$$v_y = v_{0y} + a_yt$$
$$x = x_0 + v_{0x}t + \frac{1}{2}a_xt^2$$
You can get the $v_y$ from the given angle.

3) F = ma and Newton's law of gravitation: $$F = G\frac{m_1m_2}{r^2}$$

4) F = ma and $$a_{centipetal} = \frac{v^2}{r}$$

5) Draw a diagram, and draw all the forces affecting the car.
$$F_{\mu} = \mu N$$ and $$a_{centipetal} = \frac{v^2}{r}$$

6) F = ma and Newton's law of gravitation: $$F = G\frac{m_1m_2}{r^2}$$ + $$a_{centipetal} = \frac{v^2}{r}$$, supposing I understood the question right.

 

[lolo]

thanx alot

 

[ZapperZ]

I feel like I have to keep reminding people that, per the Sticky in this section, you HAVE to show an attempt at the problem. At the very least, show that you know where you are in the subject you're doing. You should not expect the problem to be done FOR you. The MOST effective way at learning is to build upon what you ALREADY know. So these questions can best be solved by starting from the LAST place that you understand. Unless you're willing to show that, there is no way the rest of us can "help" effectively.

Zz.

 

[lolo]

i have a question, i attempted this problem but i couldn't get the correct answer.
the question is:
two friends have a combined mass of 150kg. at an ice skating rink they stand close together on skates, at rest and facing each other, with a compressed spring between them. the spring is kept from pushing them apart. when they release their arms, Al moves off in one direction at a speed of 0.539m/s, while Jo moves in the opposite direction at a speed of 0.779m/s. assuming the friction is negligible, find Al's mass.
i have this so far:
m1=Al's mass m2=Jo's mass
Vo1=0 Vo2=0
Vf1=0.539m/s Vf2=0.779m/s

m1+Vf1+m2Vf2=m1Vo1+m2Vo2
m1(0.539)+150(0.779)=0
and i got the answer to be 216.79kg

the other question i have is:
A cue ball(mass=0.165kg) is at rest on a frictionless table. the ball is hit dead center by a pool stick, which applies an impulse of 1.75Ns to the ball. the ball then slides along the table and makes an elastic head-on collision with a second ball of equal mass that is initially at rest. find the velocity of the second ball just after it is struck.
I used the formula to find Vf1 and Vf2 but its coming out to be zero
1/2m1Vf1^2 +1/2m2Vf2^2=1/2m1Vo^2+0

Vf1=(m1-m2/m1+m2)Vo1 =>0
Vf2=(2m1/m1+m2)Vo1 =>0

and one more question:
a person is making homemade ice cream. she exerts a force of magnitude 21N on the free end of the crank handle and this end moves in a circular path of radius 0.321m. the force is always applied parallel to the motion of the handle. if the handle is turned ever 1.14s, what is the average power being expended?

 

[Päällikkö]

i have this so far:
m1=Al's mass m2=Jo's mass
Vo1=0 Vo2=0
Vf1=0.539m/s Vf2=0.779m/s

m1+Vf1+m2Vf2=m1Vo1+m2Vo2
m1(0.539)+150(0.779)=0
and i got the answer to be 216.79kg

Check the bolded line again, it's got two mistakes.

a person is making homemade ice cream. she exerts a force of magnitude 21N on the free end of the crank handle and this end moves in a circular path of radius 0.321m. the force is always applied parallel to the motion of the handle. if the handle is turned ever 1.14s, what is the average power being expended?

W = Fx
P = W/t

 

[lolo]

oh, ok, it says combined mass of 150kg. ok so since they are starting from rest, wouldn't the initial velocities be zero? but I am still confused as to how to put the combined mass in the formula.

 

[marlon]

Lolo, i think you will find this link very interesting to learn Newtonian Mechanics. Let me know what you think of it :)

https://www.physicsforums.com/showthread.php?t=72040&highlight=Newtonian+mechanics

marlon