Weightless Speed: Find V for Bump Radius 35m

[sweetshelly]

Question 1:
At what speed must you go over a speed bump if people in your car are to feel weightless?
car speed V=12m/s
bump radius 35m

I don't know how to approch this problem. please help?
Question2:
A 0.075kg toy airplane if tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.21m/s in a horizontal circle of radius 0.44m
a) Find the angle the string make with the vertical
b) the tension in the string

I found the answer to a. What I did was use the formula
Thea=tan-1(Vsquare/gr)

V=1.21m/s
g=9.81m/s square
r=0.44m

So the answer is 18.7 degree

How do I slove for the tension of the string?Question 3:
A monkey swings a ball tied to a string in a circle over her head at constant speed. The ball:

a. has total force acting on it that is zero.
b. has a total force acting on it that it is not zero.
c. has an acceleration that is zero. (not C because constantly have accer because constanly changing direction)
d. has a constant velocity.

Question 4:
A box is pushed along a horizontal surface with a horizontal force that is equal in magnitude to the force of kinetic friction between the box and surface. In this case:

a. the box's speed will decrease at a constant rate.
b. the box's speed will increase at a constant rate.
c. the book will not be able to move, because the coefficent of static friction must exceed the coefficient of kinetic friction.
d. the box will move at constant speed.

 

[Astronuc]

At what sppeed must you go over the bump if people in your car are to feel weightless?
car speed V=12m/s
bump radius 35m

Kind of a strange question since it asks for speed and then it gives 12 m/s.

Think of centripetal acceleration, v²/r, which must equal the acceleration of gravity.

 

[sweetshelly]

Kind of a strange question since it asks for speed and then it gives 12 m/s.

Think of centripetal acceleration, v²/r, which must equal the acceleration of gravity.

acp=v²/r

solve (12square)/(35)= 4.11

This is not the answer because in the back of the book it say that the answer is 19m/s.

What other way can I solve this problem?

 

[Astronuc]

To be weightless on arc of R, the centripetal acceleration must = g = 9.8 m/s²,

so g = v²/R => gR = v² => v = sqrt (gR). Perhaps the textbook rounds up.

 

[sweetshelly]

To be weightless on arc of R, the centripetal acceleration must = g = 9.8 m/s²,

so g = v²/R => gR = v² => v = sqrt (gR). Perhaps the textbook rounds up.

v = sqrt (gR) = .52915

nope still not the answer we are looking for. Which in this case is 19m/s (textbook answer)

What else can we do?

 

[Astronuc]

v = sqrt (gR) = .52915

nope still not the answer we are looking for. Which in this case is 19m/s (textbook answer)

What numbers did you use?

g = 9.8 m/s² and R = 35 m.

 

[Astronuc]

How are you doing on the other problems?

So the answer is 18.7 degree

How do I slove for the tension of the string?

The 0.075kg plane produces a centripetal force in the circular plane (horizontal). Think of the formula for centripetal force.

Now the string is at some angle with respect to the plane. The tension in the string acts along the string, and it is pulling on the plane. One must find the component of centripetal force which is parallel with the string.