Lab 3/25: Cart Velocity

 

Lab 3/25: Cart Velocity

The velocity of a cart was measured by attaching a string to the end of the cart, then around a pulley and attached to several masses, giving the cart an initial velocity at a certain time. The mass of the pulley was assumed to be negligible and frictionless. The velocity was determined through video analysis. 

Results 

How do the predicted velocity and the measured velocity compare in each case? Did your measurements agree with your initial prediction? If not, why?

Both the predicted and measured velocities increased as the mass of the block increased. As the mass of the cart increased, both velocities decreased. Finally, as the distance the block dropped increased, both velocities increased. The measurements generally agreed with our predictions, but were not exactly since in each case, the measured velocity was consistently lower than the velocity predicted through the derived equation. This could be attributed to our assumption that the pulley is massless and frictionless when in actuality, the tension from the weight could have added friction to the pulley.

Does the launch velocity of the car depend on its mass? The mass of the block? The distance the block falls? Is there a choice of distance and block mass for which the mass of the car does not make much difference to its launch velocity?
 Yes, as seen between trials 4 and 7, when the mass of the car is increased and all other factors are held constant, the velocity decreases. Between trials 4 and 5, the mass of the block increased while all other factors were held constant, and the velocity increased. Similarly, increasing the distance the block falls increases the velocity. If the distance the block falls and the block mass is larger, the mass of the car will be negligible in the calculation of the launch velocity.

If the same mass block falls through the same distance, but you change the mass of the cart, does the force that the string exerts on the cart change?  In other words, is the force of the string on object A always equal to the weight of object A?  Is it ever equal to the weight of object A?  Explain your reasoning.
Yes, the force exerted on the cart varies with the mass of the cart. While the gravitational force on the block remains the same, the string's tension depends on the system's acceleration. So both the block and cart weight are a factor in the system’s acceleration. The tension isn’t equal to the weight of object A because the mass of the cart isn’t negligible and the system isn’t accelerating at g. The force will never be equal because, in a two-body system with a pulley, the string tension will always be less than the weight of the falling mass. The force will be divided between accelerating the block down and the cart forward. 

Was the frictional force the same whether or not the string exerted a force on it? Does this agree with your initial prediction? If not, why?

The frictional force was not the same whether or not the string exerted a force on the cart. When the string was pulling the cart, the frictional force could be affected by the tension in the string and the overall motion of the cart. This suggests that the frictional force is dynamic and varies with the external forces applied to the cart. If our initial prediction assumed constant friction, this result may not fully align with that assumption, as the frictional force changes depending on the forces acting on the system.

Uncertainty Calculation on Sheets

* Used "STDEV(G2:G4)" for Standard Deviation and "=SQRT(((B7-C2)^2 +(B7-C3)^2 +(B7-C4)^2)/3)" for Uncertainty