Cart Challenge - Ally and Nikki Finding the Unknown Mass

Cart Challenge - Ally and Nikki
Finding the Unknown Mass

Ally and I solved to find the mass of a variable on top of a cart. The variable we found was the weight of the soup can.

First, we weighed the mass of the cart:  .49 kg. We put the center of the cart at 110 inches and the markers on the side at 53 inches and 173 inches.


After taking 5 trials of the empty cart, the average velocity taken was .5 m/s. We then put the soup on the cart and measured the velocity. After taking 5 more separate trials, we found the average velocity with the soup can to be .25 m/s. 

Then our group needed to solve for the mass of the cart with the soup can.  We used the formula mava + mbvb = (ma + mb) (Vab).

mava + mbvb = (ma + mb) (Vab)
.49 (.5) +0 = (.49 + mb) .25
.245 = .1225 + .25mb
.1225 = .25mb
.49 kg = mb

To check our percent error, our group measured the cart with the soup can on it: 478 grams and converted it to kg: 0.478 kg

Therefore our percent error= 2.51%

To calculate the percent error:
=(.478)(.49)/ .478*100
= 2.51%

Hanging Weight UFPM post

In this lab, we had to predict where we should place a constant velocity cart so thst a falling hanging weight attached to a cart will land on a track. 

1. First, we took the masses of all of the components for the experiement.
2. Then our group calculated the time and acceleration. In order to do this, we drew our FBD's, labeling Fn, Ff, and Fg.
3. Then we calculated the sum of forces in the horizontal direction to find our Fnet.

 To find acceleration, we used A= Fnet/m


To find our mass: (then converted back into kilograms)
9.892N+.509N = 10.4N
Fnet= .509
mass= 1.04N


a = .509 / .104
a= .5 m/s^2

Then we converted the weight into kg and then into Newtons.
1kg= 100grams

buggy:4.77N
pulley: .509N
 weights: 9.892N




Then we plugged in our variables to solve for time.

x= 1/2(v)(t^2)+vi(t)
t= -1.854

In order to predict where to start the buggy, we found the velocity of the cart using a motion sensor.


To find out percent error, we took a video and tested our prediction.

The pulley landed beautifully on the cart, with a 0% error!!!

Spring Constant Practicum Challenge

Practicum Challenge: Physicists Nikki and Hank

How much does the spring have to be compressed in order for the carts to go at the same velocity?

Our group had to solve for where the two carts needed to be placed to that the carts came out with the same velocity.

Mass:

Blue= .5394 kg

Red= .55 kg

(Note: Our group weighed both carts on a scale in grams, then converted all of the measurements to kilograms)

Spring Constant:

Red= 84 N/m

Blue: 112 N/m

The following are the equations for finding the placement of where to put the blue and red carts.

Blue:

Ek=Eel

1.2mv^2= ½ kx^2

 ½ (.5394)5^2= ½ (112)x^2

.067425=56x^2

.001204m =x^2

.03469m = x

.035m or 3.5 cm=x

3.5 cm is the distance the spring is compressed for the blue and 4 cm is the distance the spring was compressed for the red. Our group solved for x by setting the Ek and Eel equations equal to each other.

Red:

Ek=Eel

1.2mv^2= ½ kx^2

½ (84)x^2=1/2 (.55)5^2

42x^2= .275

x^2= .0016369 m

x= .04045868

x= .04m or 4cm

We went to test the percent error, and the recorded velocity of both carts was .44m/s. The carts went exactly the same velocity with the distances we predicted, meaning we had a 0% trial error. :) This challenge taught us how to use formulas to solve for a variable and how to manipulate data. Hank and I solved for the distance, converted units, found the mass, and applied to Ek and Eel formulas we learned in the FINAL challenge of the year.