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5.2 Dynamics and Newton’s Second Law NOTES
AP Physics
Earlier when we looked at motion in 2 dimensions for conditions of constant
acceleration, we found that time was the link between the x direction and the y
direction.
In dynamics problems that are not in equilibrium, Newton’s Second Law (F =
ma) provides a link between forces and kinematics. Many problems in
mechanics are of two general types: Either we start with kinematics (velocity,
acceleration, etc) and we want to determine forces or we start with forces and
want to determine kinematics (velocity, acceleration, etc).
The approach to these problems consists of:
1.) Sketch an overview of:
a.) list of values that identifies known quantities and what the problem is
trying to find.
b.) A free-body diagram that shows all forces acting on the object.
2.) If kinematics is used to find velocities or positions, also need:
a.) motion diagram to determine the direction of acceleration.
b.) pictorial representation that establishes a coordinate system, shows
important points in that motion, and defines symbols.
3.) Solve: Write Newton’s second law in component form as:
Fx  ma x
Fx  ma x
Depending on the problem, either:
Solve for the acceleration, then use kinematics to find velocities and
positions.
Use kinematics to determine the acceleration, then solve for unknown
forces.
4.) Assess: Check that the result has the correct units, is reasonable, and
answers the question.
Example 1 A rope connected to a 50-kg sled pulls it along a frictionless sheet
of ice. The tension in the rope is 100 N, and the rope is oriented at
an angle of 300 above a line drawn parallel to the ice. Calculate the
horizontal acceleration of the sled.
Example 2 A 20-kg block is pulled on a horizontal frictionless surface by a
rope that makes an angle of 370 with the horizontal. Calculate the
tension in the rope if the block accelerates at 2.0 m/s2.
Example 3 A tennis ball of mass 0.048 kg traveling at 25 m/s in the horizontal
direction hits a practice wall and rebounds in the opposite direction
at 20 m/s. Calculate (a) the ball’s average acceleration and (b) the
magnitude and direction of the average force on the wall on the ball
if the force acts for 0.060 s.
Example 4 A 3.1 g penny thrown from the top of the Sears building in Chicago
lands on the head of a passerby 460 m below. Just before the penny
hits the person’s head, it is falling at a speed of 25 m/s. It is stopped
by the head in a distance of 1.0 mm. (a) Calculate the deceleration
of the penny. (b) Calculate the force of the penny on the head. (c)
Parts of the skull bones will be fractured by forces of about 900 N
or more. Is there a chance of fracturing the skull with the penny?