Cart on a Ramp
Purpose:
The purpose of this lab is to collect distance, velocity, and acceleration data as a cart rolls up and down a ramp, and to analyze the position vs. time, velocity vs. time, and acceleration vs. time graphs. We did this lab also to determine the best fit equations for the distance vs. time and velocity vs. time graphs and to determine the mean acceleration from the acceleration vs. time graph.
Materials:
LabQuest
(and LabQuest app)
Motion detector
Motion detector
bracket
Ramp
Dynamics cart
A bumper (to keep the cart from rolling off the end of the track)
Procedure:
1. Prepare the track and motion detector for data collection.
Attach the motion detector bracket to the track.
Attach the motion detector to the motion detector bracket.
Adjust the position of the motion detector bracket so the motion detector is 0.15m from the end of the track.
Set the switch on the motion detector to the track position.
2. Connect the motion detector to DIG 1 of LabQuest and choose "New" from the file menu.
3.Place the cart on the track near the bottom end stop. If your cart has a plunger, face the plunger away from the motion detector. Start data collection. You will notice a clicking sound from the motion detector. Wait about a second, then briefly push the cart up the ramp, letting it roll freely up nearly to the top, and then back down. Catch the cart as it nears the end stop.
4. Examine the position vs. time graph. Repeat Step 3 if your position vs. time graph does not show an area of smoothly changing distance. Check with your instructor if you are not sure whether you need to repeat data collection.
Data/Analysis
The purpose of this lab is to collect distance, velocity, and acceleration data as a cart rolls up and down a ramp, and to analyze the position vs. time, velocity vs. time, and acceleration vs. time graphs. We did this lab also to determine the best fit equations for the distance vs. time and velocity vs. time graphs and to determine the mean acceleration from the acceleration vs. time graph.
Materials:
LabQuest
(and LabQuest app)
Motion detector
Motion detector
bracket
Ramp
Dynamics cart
A bumper (to keep the cart from rolling off the end of the track)
Procedure:
1. Prepare the track and motion detector for data collection.
Attach the motion detector bracket to the track.
Attach the motion detector to the motion detector bracket.
Adjust the position of the motion detector bracket so the motion detector is 0.15m from the end of the track.
Set the switch on the motion detector to the track position.
2. Connect the motion detector to DIG 1 of LabQuest and choose "New" from the file menu.
3.Place the cart on the track near the bottom end stop. If your cart has a plunger, face the plunger away from the motion detector. Start data collection. You will notice a clicking sound from the motion detector. Wait about a second, then briefly push the cart up the ramp, letting it roll freely up nearly to the top, and then back down. Catch the cart as it nears the end stop.
4. Examine the position vs. time graph. Repeat Step 3 if your position vs. time graph does not show an area of smoothly changing distance. Check with your instructor if you are not sure whether you need to repeat data collection.
Data/Analysis
Conclusion:
In doing this lab, I hoped to learn the position, velocity, and acceleration of a gently pushed cart on a ramp. I'd say I was successful.
1. How closely does the slope correspond to the acceleration?
Acceleration is equivalent to the slope of velocity. The acceleration is .22823m/s/s, and the slope of the velocity graph is .22823m/s/s. They are the exact same thing.
2. What was the velocity of the cart at the top of its motion?
The car wouldn't have a velocity. This was when the car was closest to the motion detector. The car had to stop before it could start rolling back down again, so when the car stops, it logically can't have any velocity because it's not moving, therefore when the cart is at the top of its motion, it has no velocity.
3. What was the acceleration of the cart at the top of its motion.
As in question 2, the car would have no acceleration. The car had to stop before it could roll down again. The car had to slow down before it could start picking up speed again. So when it's at its highest point, the car is not moving, thus its acceleration is zero.
4. Is the cart's acceleration constant during the free-rolling segment?
Yes. As an object rolls down a hill, or even if it's simply dropped, the object will pick up speed at a constant rate, because the rate of gravity is constant, regardless if the object is rolling down a ramp or being dropped. Looking at the graph, you wouldn't think that the acceleration is constant, but that is only because the numbers and intervals are so small and zoomed in, the acceleration looks more ragged than it really is. It's like if you look a piece of paper. Smooth right? But if you put it under a microscope, the paper looks more like a mountain range.
5. Review your preliminary questions, based on your new knowledge, do you still agree with your prediction? Why or why not?
Looking back at my predictions, the only one that even remotely resembled the graphs above was the position vs. time graph. This is probably because I've been working with position vs. time graphs for a long time, so I can picture them pretty easily. The velocity and acceleration graphs, on the other hand, are more new to me, so the graph predictions weren't very accurate. However, as I work with them more and more, they are starting to become clearer and easier for me to analyze and create.
6. Explain what the meaning of the equation that you found for the velocity vs. time graph. Label each variable and explain what the meaning of the slope is.
You can use the equation y=mx+b to find the slope for any graph. I used this equation to find the slope of the velocity. First you pick any point on the graph and fill in the value for x and y. You also fill in for the y-intercept (b), which happens to be 0.7507. From there you just solve for m (the slope), which happens to be 0.22823. The slope is the rate at which the object moves or accelerates, which is why it makes sense that it's the same thing as acceleration.
7. Predict what the position vs. time, velocity vs. time, and the acceleration vs. time would be for an object that was falling straight down, rather than being on an incline.
Position vs. Time: the graph would be a curved line going upward in the positive direction
Velocity vs. Time: the graph would be a straight line going upward in the positive direction.
Acceleration vs. Time: the graph would be a straight, horizontal line going in the positive direction.
In doing this lab, I hoped to learn the position, velocity, and acceleration of a gently pushed cart on a ramp. I'd say I was successful.
1. How closely does the slope correspond to the acceleration?
Acceleration is equivalent to the slope of velocity. The acceleration is .22823m/s/s, and the slope of the velocity graph is .22823m/s/s. They are the exact same thing.
2. What was the velocity of the cart at the top of its motion?
The car wouldn't have a velocity. This was when the car was closest to the motion detector. The car had to stop before it could start rolling back down again, so when the car stops, it logically can't have any velocity because it's not moving, therefore when the cart is at the top of its motion, it has no velocity.
3. What was the acceleration of the cart at the top of its motion.
As in question 2, the car would have no acceleration. The car had to stop before it could roll down again. The car had to slow down before it could start picking up speed again. So when it's at its highest point, the car is not moving, thus its acceleration is zero.
4. Is the cart's acceleration constant during the free-rolling segment?
Yes. As an object rolls down a hill, or even if it's simply dropped, the object will pick up speed at a constant rate, because the rate of gravity is constant, regardless if the object is rolling down a ramp or being dropped. Looking at the graph, you wouldn't think that the acceleration is constant, but that is only because the numbers and intervals are so small and zoomed in, the acceleration looks more ragged than it really is. It's like if you look a piece of paper. Smooth right? But if you put it under a microscope, the paper looks more like a mountain range.
5. Review your preliminary questions, based on your new knowledge, do you still agree with your prediction? Why or why not?
Looking back at my predictions, the only one that even remotely resembled the graphs above was the position vs. time graph. This is probably because I've been working with position vs. time graphs for a long time, so I can picture them pretty easily. The velocity and acceleration graphs, on the other hand, are more new to me, so the graph predictions weren't very accurate. However, as I work with them more and more, they are starting to become clearer and easier for me to analyze and create.
6. Explain what the meaning of the equation that you found for the velocity vs. time graph. Label each variable and explain what the meaning of the slope is.
You can use the equation y=mx+b to find the slope for any graph. I used this equation to find the slope of the velocity. First you pick any point on the graph and fill in the value for x and y. You also fill in for the y-intercept (b), which happens to be 0.7507. From there you just solve for m (the slope), which happens to be 0.22823. The slope is the rate at which the object moves or accelerates, which is why it makes sense that it's the same thing as acceleration.
7. Predict what the position vs. time, velocity vs. time, and the acceleration vs. time would be for an object that was falling straight down, rather than being on an incline.
Position vs. Time: the graph would be a curved line going upward in the positive direction
Velocity vs. Time: the graph would be a straight line going upward in the positive direction.
Acceleration vs. Time: the graph would be a straight, horizontal line going in the positive direction.