Objectives

In this lab, you will create force diagrams and then use them to predict motion. This is a consequence of Newton’s Second Law and is a valuable skill to hone. The model of friction as presented in your textbook is a simplified version of the very messy and complicated experimental friction phenomena. In this lab, you will construct the model of friction from your data, and it may differ from the book’s treatment of the concept in places.

For the following activities, you will use a physics simulation program. Visit: https://uglabs.physics.ucr.edu/ for lab downloads and links.

Introduction:

Newton’s Laws can be difficult to apply to solve complex physics problems. When used in combination, though, they can describe motion within a system very precisely. Newton’s 1st Law describes how to make one object move. It states that a net force from external sources (i.e. other objects) will make one object change its motion. This is how Newton defined what forces do. If there is no net force on the object, then it will continue on with its original speed and direction without change (this includes the case where the original motion is zero). Newton’s 2nd Law establishes a mathematical representation by stating how much of a change in velocity you will get by applying external force on an object.

Newton’s 3rd Law discusses how objects interact with each other. For example, if I give another object a force, it will give the same magnitude force back to me. Note that this reaction force that is described by Newton’s 3rd Law does not affect the motion of the original object I am trying to move. Newton’s 1st and 2nd Laws are specifically dependent on the forces acting on that object and not what force is coming back to me. Also note that Newton’s 3rd Law does not predict the motion of the object, only one particular force between two things.

1. Static Friction

1.1: In this section, you will use the cart and track. Consider the cart on the track that is stationary at a certain angle, θ. You can call the mass of the cart, M and the acceleration due to gravity, g. Draw a free-body diagram for all the forces acting on the cart.

1.2: Write down two separate equations for Newton’s second law with static friction: one for forces pointing along the track and one for forces pointing perpendicular to the track. Do some forces appear in only one of the equations? For forces that have some component in both, make sure you break down those force vectors correctly in the equation.

1.3: Assuming the cart remains stationary, solve for the static friction force in terms of M, g, and θ. How does it change if the angle increases slightly (does it increase, decrease or remain the same)?

1.4: Now we will turn to the simulation. Click on the cart to find the mass of the cart (this is M). Turn on the friction pad by clicking on the button right next to the words “friction pad.”

1.5 By tilting the track at different angles, you can change the magnitude of the component of the gravitational force acting parallel to the track. If the downhill gravitational force is larger than the maximum value of the static friction force, the cart will slide downhill. What is the largest angle (called the critical angle) that the track can have before the cart starts to slide?

1.6: Carefully and slowly increase the angle of the track until the cart slips. Measure or calculate the critical angle. Repeat the measurement two more times, then average the value and estimate its uncertainty.