Consider the apparatus shown below: Data: Mass Block A (m a) = 0.5 kg Mass Block
ID: 1635466 • Letter: C
Question
Consider the apparatus shown below:
Data:
Mass Block A (ma) = 0.5 kg
Mass Block B (mb) = 0.75 kg
Mass Pulley (mp) = 0.24 kg
Radius Pulley (rp)= 0.6 cm
g = 9.8 m/s2
Measuring tools available:
Metric ruler
Stop watch
The goal of the experiment is to find the coefficient of kinetic friction (k) between Block A and the surface using only the stopwatch and the metric ruler.
Block B was dropped from several different positions, and the time to reach the ground was measured.
Data Collected
Distance from the ground to Block B (m)
Time for Block B to hit the ground (s)
1.2
0.45
1.0
0.42
0.8
0.37
0.6
0.32
0.4
0.26
The work-energy relation for this scenario is: K1 + U1 + Wother = K2 + U2
The tension in the rope does ___________(positive or negative) work on Block A. and ___________(positive or negative) work on Block B. The net work done by the tension in the rope is ____________. (positive, negative, or zero)
When the Block is released, which block will move faster?
Block A
Block B
Both will move with same speed.
K1 = zero (released from rest)
Kinetic friction does work on Block A, so Wother = Wf = -kmagd.
Procedures:
Write expressions for the potential energies U1 and U2.
U1 =
U2 =
Write an expression for K2 (should have three terms):
K2 = ______________+ _____________+ ___________
The third term in the equation above contains the rotational terms I and .
Make the necessary substitutions to eliminate .
Solve the equation for velocity as a function of distance.
v = (This side of the equation will have the variables g, d. ma, mb, k , I and r.) There may also be a constant, and some of the variables may be raised to a power.
Hint: This problem appears at the end of Chapter 9. (It is Problem 73 on page 292.) The good news is that the answer is in the back of the book. The bad news is that the answer provided (although close) is not correct. The answer in the back of the book is correct for v2, so to get v, take the square root of both sides.
Notice that the equation does not have the time variable in it even though time is one of the measured variables. Make the necessary substitution to eliminate v (this was not measured) and insert time. Remember, velocity = distance /time. The equation contains the two variables that were measured (i.e., distance and time).
You will now figure out how to plot the variables so that the equation is a straight line and k is in the expression for slope.
Remember, the general equation for the slope of a line is y = mx + b. Here b is the y-intercept and is zero. Choose what x and y should represent. The slope is the coefficient in front of x.
Some possibilities: (x = t, y = d), (x = t, y = d2), (x = t2, y = d). Plus, there are many more. Hint: One of the choices above is the best to use.
Open Excel and make a new workbook.
Put the given data above in a table.
Do any additional calculations necessary.
Create a linear Scatter Graph using the data in the table.
Make sure the graph has the required parts: labels on the axes, units, and a title.
Use the Trend line option to display the equation of the line on the graph.
Find the slope from the equation (the coefficient of the x variable).
Use algebra to solve the equation for the coefficient of kinetic friction, k.
Create the equation in the Excel workbook using dynamic variables.
Solve the equation for k.
Distance from the ground to Block B (m)
Time for Block B to hit the ground (s)
1.2
0.45
1.0
0.42
0.8
0.37
0.6
0.32
0.4
0.26
Explanation / Answer
Work done by a force is positive if the force and displacement are in the same direction and negative if they are in opposite direction. Tension is always directed away from the block and towards the pulley; displacement of block A is towards pulley while that of block B is away from the pulley.
Therefore:
The tension in the rope does positive work on Block A. and negative work on Block B. The net work done by the tension in the rope is zero.
When the Block is released, which block will move faster?
Both will move with same speed.