Circular Motion and Energy Calculations

[kelvin56484984]

Homework Statement

A)
An object moving along the x-axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m?
B)
A 50-kg child riding a Ferris wheel (radius of wheel R = 10 m) travels in a vertical circle. The wheel completes one revolution every 10 s. What is the magnitude of the force on the child by the seat at the highest point on the circular path?
C)
A 0.50-kg mass attached to the end of a string swings in a vertical circle (radius = 2.0 m). When the mass is at the lowestpoint on the circle, the speed of the mass is 12 m/s. What is the magnitude of the force of the string on the mass at this position?
D)
A 2.5-kg object falls vertically downward by 80 cm. How much work is done by the gravitational force on the object in this process?
E)
If vector A and B have magnitudes 12 and 15, respectively, and the angle between the two when they are drawn starting from the same point is 110, what is the scalar product of these two vectors?

Homework Equations

a=v^2/r
W=Fd
T=2*pi*r/v

The Attempt at a Solution

A)
positive area + negative area
1/2*20*4+1/2*(-10)*2
=30J

B)
T=2*pi/V
V=6.28 m/s
mg-N=m(v^2)/R
N=50*9.8-50*(6.28^2)/10
N=0.29kN

C)
T-mg=mv^2/R
T=(0.5*8^2)/2 +0.5*9.8
T=41N

D)
W=-(2.5*9.8*0.8)
W=-20J

E)
15*12*cos110
=-62

It said one of my answer is wrong .
Thank you

 

[TSny]

Welcome to PF!

Hint: The sign is incorrect for one of your answers.

 

[kelvin56484984]

For part D
It should be mgh instead of -mgh?

 

[TSny]

To make sure you understand the sign of the work, use the definition of work: W = F d cosθ. For part D, what would be the values for F, d and θ?

 

[kelvin56484984]

F is mg
d is height
And θ is 0 degree?
If the object is raise up , the workdone is -mgh?
the θ also remain 0 but the g become negative?

 

[TSny]

F is mg
d is height
And θ is 0 degree?

Yes

If the object is raise up , the workdone is -mgh?
the θ also remain 0 but the g become negative?

No, g is always a positive number. θ ≠ 0^o for this case. θ is the angle between the force direction and the displacement direction.

 

[kelvin56484984]

What is the force direction and the displacement direction when it raises up?
normal force (force direction,upward) and moving upward(displacement direction)?
How can I get the θ is 180?

 

[TSny]

What is the force direction and the displacement direction when it raises up?
normal force (force direction,upward) and moving upward(displacement direction)?
How can I get the θ is 180?

What is the direction of the force of gravity if the object is moving upward?

 

[kelvin56484984]

the force of gravity is putting downward
So the force is gravity force instead of normal force in this case?

 

[TSny]

If you are finding the work done by the force of gravity, then you use the force of gravity. If you want the work done by the lifting force, then you use the lifting force.

 

[kelvin56484984]

Thank you
I get it

 

[TSny]

Good work