A 1.4-kg object moves along the x axis, subject to the potential energy shown in the figure. If the object's speed at point B is 1.70 m/s, what are the approximate locations of its turning points?
___________m (left-hand turning point)
___________m (right-hand turning point)
*** The graph plots points of Joules vs m (W vs d)... it starts at A(0m, 10.0J) and goes down to B(2.0J, 2.0m) and then goes back up to C...
To determine the approximate locations of the turning points, we need to examine the potential energy graph provided.
First, let's analyze the given information:
- The object's mass is 1.4 kg.
- The object's speed at point B is 1.70 m/s.
- The potential energy graph starts at point A (0m, 10.0 J), goes down to point B (2.0 J, 2.0 m), and then goes back up.
The turning points on the potential energy graph occur where the slope of the graph is zero. At these points, the object changes its direction of motion.
To find the turning points, we can calculate the first derivative of the potential energy function. The first derivative gives us the slope of the graph at any point.
Let's represent the turning points as (x_Left, y_Left) and (x_Right, y_Right).
1. Calculate the slope at point B:
We are given the potential energy at point B as 2.0 J, which corresponds to the vertical axis. The slope can be approximated as:
Slope at B = (change in y) / (change in x) = (2.0 J - 10.0 J) / (2.0 m - 0 m) = -8.0 J/m
2. Find the left-hand turning point:
To find the left-hand turning point, we need to find the point where the slope on the left side of point B (to the left of B) is zero.
Start from point B and move to the left until you reach a point where the slope is approximately zero. This point will give us the left-hand turning point.
3. Find the right-hand turning point:
To find the right-hand turning point, we need to find the point where the slope on the right side of point B (to the right of B) is zero.
Start from point B and move to the right until you reach a point where the slope is approximately zero. This point will give us the right-hand turning point.
Note: Since the graph is not provided, we cannot provide specific values for the turning points. You will have to analyze the graph based on the information provided to determine the approximate locations of the turning points.