Question

the object has a mass of 7.0 kg. what is the potential energy of the object at point a?
g = 10.00 m/s²
height (m) vs. time (s)
chart: x-axis time (s) from 0 to 4, y-axis height (m) from 0 to 8. line starts at (0,6), peaks at (0.5,8), then at t=1, height is 6 (point a), goes to (2.5,0), then back to (4,6).
options: 420 j, 42 j, 210 j

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy (PE) is $PE = mgh$, where $m$ is the mass, $g$ is the acceleration due to gravity, and $h$ is the height.

Step2: Identify the values from the problem

We know that $m = 7.0\ kg$, $g = 10.00\ m/s^2$, and from the graph, the height at point A ($h$) is 6 m.

Step3: Substitute the values into the formula

Substitute $m = 7.0\ kg$, $g = 10.00\ m/s^2$, and $h = 6\ m$ into the formula $PE = mgh$.

$$ PE = 7.0\ kg\times10.00\ m/s^2\times6\ m $$

Step4: Calculate the potential energy

First, multiply 7.0 and 10.00: $7.0\times10.00 = 70$. Then multiply the result by 6: $70\times6 = 420$? Wait, no, wait. Wait, 7.0 kg 10.00 m/s² is 70 N, and then 70 N 6 m is 420 J? But wait, let me check again. Wait, 7106 = 420? Wait, but the options have 420 J, 42 J, 210 J. Wait, maybe I made a mistake in the height. Wait, looking at the graph: the y-axis is height (m), and point A is at (1,6), so height is 6 m. Mass is 7 kg, g is 10. So 7106 = 420. But wait, maybe the height is 6? Wait, but let me check the calculation again. 710=70, 706=420. So the potential energy is 420 J? Wait, but let me confirm the formula. Gravitational potential energy is indeed $mgh$. So with m=7, g=10, h=6, then PE=7106=420 J.

Answer:

420 J