Your vertical spring accelerometer has a 200 g mass hanging from it. You climb aboard the roller coaster and watch the accelerometer read 0.4 g for 3 seconds while descending the first peak and then change to 1.5 g for 2 seconds while climbing the second peak. Your fully loaded car is 2000 kg.
a. What is your acceleration going down, and what is it going up in m/s^2?
b. Calculate your final velocity going down and going up.
How would I go about solving this? Thank you ~
To solve this problem, we need to use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = m*a). Since the mass is constant, we can rearrange the equation to solve for acceleration, which is what we need to find.
Let's start with part a:
a. What is your acceleration going down, and what is it going up in m/s^2?
Given:
Mass of the hanging object (m1) = 200 g = 0.2 kg
Initial acceleration going down (a1) = 0.4 g
Time going down (t1) = 3 s
Acceleration going up (a2) = 1.5 g
Time going up (t2) = 2 s
Mass of the fully loaded car (m2) = 2000 kg
First, let's convert the acceleration in terms of gravity (g) to m/s^2:
1 g = 9.8 m/s^2
Acceleration going down:
a1 = 0.4 g = 0.4 * 9.8 m/s^2 = 3.92 m/s^2
Acceleration going up:
a2 = 1.5 g = 1.5 * 9.8 m/s^2 = 14.7 m/s^2
b. Calculate your final velocity going down and going up.
To find the final velocity, we can use the following equation:
Final velocity (v) = Initial velocity (u) + (acceleration * time)
Going down:
Initial velocity (u1) = 0 (assuming the object starts from rest)
Acceleration (a1) = 3.92 m/s^2 (from part a)
Time (t1) = 3 s (given)
v1 = u1 + (a1 * t1)
v1 = 0 + (3.92 * 3)
v1 = 11.76 m/s
Going up:
Initial velocity (u2) = 11.76 m/s (the final velocity from going down becomes the initial velocity going up)
Acceleration (a2) = 14.7 m/s^2 (from part a)
Time (t2) = 2 s (given)
v2 = u2 + (a2 * t2)
v2 = 11.76 + (14.7 * 2)
v2 = 41.16 m/s
Therefore, the final velocity going down is 11.76 m/s, and the final velocity going up is 41.16 m/s.
To solve this problem, we can use the concept of the accelerometer and the equation for acceleration.
a. Acceleration going down:
The accelerometer reads 0.4 g while descending the first peak. We need to convert this to m/s^2 as acceleration is typically measured in SI units.
1 g is equal to the acceleration due to gravity, approximately 9.8 m/s^2. So, 0.4 g is equal to 0.4 * 9.8 m/s^2 = 3.92 m/s^2.
Therefore, the acceleration going down is 3.92 m/s^2.
Acceleration going up:
The accelerometer reads 1.5 g while climbing the second peak. Again, we need to convert this to m/s^2.
1.5 g is equal to 1.5 * 9.8 m/s^2 = 14.7 m/s^2.
Therefore, the acceleration going up is 14.7 m/s^2.
b. To calculate the final velocity, we can use the equations of motion.
Downward motion (going down the first peak):
We know the initial velocity (0 m/s) and the acceleration (3.92 m/s^2), and we need to calculate the final velocity.
The equation for final velocity (v) in terms of initial velocity (u), acceleration (a), and time (t) is:
v = u + at
Substituting the given values:
v = 0 + (3.92 m/s^2) * 3 s = 11.76 m/s.
Therefore, the final velocity going down is 11.76 m/s.
Upward motion (going up the second peak):
We know the initial velocity (11.76 m/s) (due to the first peak) and the acceleration (14.7 m/s^2), and we need to calculate the final velocity.
Using the same equation:
v = u + at
Substituting the given values:
v = 11.76 m/s + (14.7 m/s^2) * 2 s = 41.16 m/s.
Therefore, the final velocity going up is 41.16 m/s.