A single conservative force = (6.0x - 12) N where x is in meters, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 23 J at x = 0.
(a) Write an expression for U as a function of x, with U in joules and x in meters.
U(x) =

(b) What is the maximum positive potential energy?
J

(c) At what negative value of x is the potential energy equal to zero?
m

(d) At what positive value of x is the potential energy equal to zero?
m

1. 👍 0
2. 👎 0
3. 👁 2,509
1. ΔU = U(x) - U(0) = ∫(6x - 12)dx
Therefore, with U(0) = 23 J, we obtain by integrating
U = 23 + 12x - 3x ²
F = 0 when 6x - 12 = 0
Thus x = 2 m
Substituting into U = 23 + 12x² - 3x ,
U = 35 J
Using the quadratic equation find the negative and positive values of x for which U = 0
3x ² - 12x-23 =0
x=(12±sqrt(144+4•3•23)}/2•6
x = -1.42 m
x = 5.42 m

1. 👍 0
2. 👎 1

## Similar Questions

1. ### physics

true or false If a net force acts on an object, the object's speed will change. An object's velocity will change if a net force acts on the object. If two object have the same acceleration, they are under the influence of equal

2. ### Physics

This is probably a really easy question, but I just don't know how to set it up. An object in equilibrium has three forces exerted on it. A 33 N force acts at 90 degrees from the x-axis and a 44 N force acts at 60 degrees. What

3. ### Physics

A single conservative force acts on a 5.00 kg particle. The equation Fx = (2x + 4) N describes this force, where x is in meters. As the particle moves along the x axis from x = 1.40 m to x = 5.80 m, calculate the following. (a)

4. ### IB PHYSICS

An object in equilibrium has three forces exerted on it. A 30 N force acts at 90° from the x-axis and a 44 N force acts at 60° from the x-axis. What are the magnitude and direction of the third force? NO IDEA WHERE TO START

1. ### Physics

A force of 3.00N acts through a distance of 12m in the direction of the force.Find the work done. work= force *distance If force is in newtons, distance in meters, the work unit is in joules.

2. ### Physics

A force of 3.00 N acts through a distance of 12 m in the direction of the force.Find the work done. If I recall correctly, work=force*distance. The units should be newton-meters. 3*12=36

3. ### Physics

Three forces act on an object. A 4 N force acts due east and a 3 N force acts due north. If the net force on the object is zero, what is the magnitude of the third force?

4. ### Physics

Three forces act on the object.A 3- N force acts due west, and 4-N force acts due south.If the net force on the object is zero ,what is the magnitude of the third force

1. ### physics

The meter stick in the drawing can rotate about an axis located at the 20.0-cm mark. The axis is perpendicular to the screen. A force F acts at the left end; the force is perpendicular to the meter stick and has a magnitude of 175

2. ### physics

A force acting on a particle moving in the xy plane is given by Fx = (2yi +x^2j)N, where x and y are in meters. The particle moves from the origin to a final position having coordinates x=5.00m and y=5.00m, as in Fig. Calculate

3. ### Physics

A boy pulls a sled with a force of 40N on a rope 2.5 meters long. The end that he holds is 1.5 meters higher than the end attached to the sled. What is the magnitude of the horizontal component that acts to pull the sled forward?

4. ### physics

A 2.25 kg ball experiences a net force of 965 N up a ramp. Once the ball reaches the top of the ramp, the force no longer acts. The force acts over a distance of 1.50 m on the ramp. Find the horizontal distance x that the ball