PhysicsLAB Lab
Mass of a Rolling Cart

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The purpose of this experiment is to determine the unknown mass of a rolling cart using two photogates separated by a given distance, a known hanging mass, a frictionless pulley system, and an incline plane. Care needs to be taken that the string remains parallel to the surface of the incline.
During the experiment, the cart will initially start from rest. When the suspended mass is gently released, the cart, with its card of known length, will pass through each of the two photogates. The students will then be given the time required for the card to pass through each of the photogates. They need to also measure the distance between the photogates, the incline's angle of inclination, and record the mass of the hanging weight.
From this information they will be asked to show any freebody diagrams and calculations they use to determine the experimental mass of the cart. A percent error will then be calculated against the correct value.
Refer to the following information for the next four questions.

General Data
hanging mass in kilograms 

distance between photogates in meters 

length of card in meters 

plane's angle of inclination in degrees 

Photogate Start Time End Time
Refer to the following information for the next two questions.

On your papers, draw two draw a freebody diagrams: one for the cart (m) and the other for the hanging mass (M). Then fill in the blanks provided with the generalized equations of motion for each object. Do not substitute in numerical values, you may use the variables: a, T, m, M, g, and theta.
hanging mass' equation 

rolling cart's equation 

Refer to the following information for the next three questions.

Now determine the average velocity of the cart as it passes through each of the photogates and then its average acceleration up the incline.


a = 

Refer to the following information for the next question.

Using your previously stated system of equations, solve for the rolling cart's mass in kilograms. Show all of your calculations on your papers.
cart's mass in kilograms 

Refer to the following information for the next question.

Once you have obtained your experimental value for the cart's mass, ask Mrs. Colwell for its measured value. Calculate a percent error for your experiment.
your experiment's percent error 

Your lab report should include your freebody diagrams and all of your calculations neatly organized and presented. Make sue that all numerical answers have appropriate units.

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Catharine H. Colwell
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