Download Newton`s Laws Worksheet

Newton’s Laws Worksheet
NII on a level surface with friction
1. What is kinetic friction? What is the formula for kinetic friction? In Figure 1, draw the
force vector representing the friction and write the formula next to it.
2. What is the normal force? In what situations do you have a normal force? In what
situations do you not have a normal force? In Figure 1 draw the normal force vector.
3. What is the equation for weight? In what situations do we have weight? In Figure 1
draw the weight vector and write the formula next to it.
50 Newtons
m1 = 5 kg
Figure 1
For this figure we have now drawn all of the forces. Now we will apply Newton’s second
law to the figure above. Note that there is already a force of 50 Newtons action on the box.
4. For the motion above draw an appropriate coordinate system. Label which directions are
positive and which are negative.
5. What is Newton’s second law? What is Newton’s second law in component form?
Define all of the variables.
6. Apply Newton’s second law to all of the forces acting in the x-direction in Figure 1. Do
not substitute any numbers for variables at this point.
Fx =
7. Apply Newton’s second law to all of the forces acting in the y-direction in Figure 1. Do
not substitute any numbers for variables at this point.
Fy =
8. What do you know about the acceleration in the y direction (ay)?
9. Find the Normal force of the block. To do this, use the equations you just derived from
NII.
10. Find the acceleration of the block. To do this, use the equations you just derived from
NII. First substitute the formula for kinetic friction that you wrote down in #1 into the x
equation. Next, take the value (or equation) of the normal force you found in #9 and
substitute it into the x equation. Assume a  = 0.42.
a = 5.88 m/s2
NII with Tension
11. What is tension? In what problems do we apply tension to? In Figure 2 draw the force
vectors representing tension.
m1 =
20 kg
m2
= 7 kg
Figure 2
13. In Figure 2 what other forces are acting on the blocks? Draw these forces on the diagram
above.
14. Apply NII to the first block, m1. Do this by first drawing a separate free-body diagram of
m1 below. Label this diagram with the coordinate system you choose and the directions
of positive and negative. Positive is usually in the direction of motion. Apply NII for
both the x and y directions. Do not substitute any numbers for variables at this point.
Fx1 =
Fy1 =
15. Apply NII to the second block, m2. Do this by first drawing a separate free-body diagram
of m2 below. Label this diagram with the coordinate system you choose and the
directions of positive and negative. Positive is usually in the direction of motion. Do the
coordinate systems for both blocks have to be the same? Apply NII for both the x and y
directions. Do not substitute any numbers for the variables at this point.
Fx2 =
Fy2 =
16. Based on the equations for both masses, what do we know about the accelerations in the
x directions? What do we know about the accelerations in the y directions?
17. Based on your answers in #16, rewrite the x and y equations for the blocks and substitute
in the any numbers you know for the accelerations. Now, solve each equation for the
acceleration in that equation. Based on your answer in #16, set the appropriate equations
equal to each other. Now, what do we know about the tensions? Solve for the tension.
T = 101.6 N
18. Once you have solved for the tension, use that number to solve for the acceleration using
one of the equations you derived in #14 and #15.
a = 4.72 m/s2
NII for an Incline Plane (no friction)
1. For the triangle below, label each side in terms of the hypotenuse and the angle .
Assume  = 25

wt = mg
2. As we have done in the previous two examples, label the forces in Figure 3. Draw an
appropriate coordinate system as well.
m1 = 10 kg
 = 25
Figure 3
3. Apply NII to the block above.
Fx =
Fy =
4. Based on the equations derived above, determine the normal force.
5. Based on the equations above, determine the acceleration down the incline.
a = 4.15 m/s2
6. If there were a frictional force in this problem, what does the coefficient of friction have
to be for the block to move with a constant velocity? This question will require you to
alter your Fx equation.
 = 0.47
The next problem is for you to do over the weekend. Please hand in this completed worksheet
on Monday. This problem will utilize all of the things learned from the previous problems.
M2 = 5 kg
 = 30
M3 =
3 kg
M1 = 20 kg
The arrows represent the direction of motion.
Question: What is the acceleration of the system? a = 6.832 m/s2
HINTS:
1. The tensions on the left side of M2 are equal, and the tensions on the right side of M2 are
equal. Label the left side tensions T1 and the right side tensions T2. T1  T2.
2. You will yield three useful equations. Two of the equations will only have one tension in
them while the third equation will have both tensions in them. Take the two equations
with only one tension and solve for tension. Plug these equations into the third equation
for the tensions. This will eliminate the tensions. Another way to do this is to add all
three equations together.