1. Solving problems when  F = ma

2. The cyclist has a mass of 50 kg and is accelerating at 0.9 m/s2.
What is the size of the unbalanced force acting on the cyclist?

3. How to approach a dynamic problem:
Draw a free-body diagram
Choose a coordinate axis and resolve all forces into components.
Set the sum of the force components each equal to ma.
Solve the resulting equations for the unknowns.

4. Draw a free-body diagram Add all forces in one direction together (x?)
Read the problem.
(identify givens, look for “hidden” knowledge)
Draw a free-body diagram
(identify all forces acting upon object)
Add all forces in one direction together (x?)
 F = F1 + F2 + F3 + …
(determine sum of forces, maybe Fnet = 0 or Fnet = ma)
Add all forces in other direction together (y?)
Solve for what you don’t know

5. If each person is pushing forward against the 1,500 N car, find:
The Normal force
The acceleration of the car

6. If the 10 Newton crate is being pushed forward by a
force P of magnitude 80 N at an angle of 300 as shown
find:
The mass of the crate
The Normal force
The acceleration of the crate

7. If m1=20 kg and m2=70 kg find:
The tension in the cable
The acceleration of the masses

8. Given: The car is accelerating forward at 2m/s2 and  = 25°
Find: The forces in the ropes AB
and AC.

9. A stream of water strikes a stationary turbine blade, as the drawing
illustrates. The incident water stream has a velocity of m/s,
while the exiting water stream has a velocity of m/s. The mass
of water per second that strikes the blade is 25.0 kg/s. Find the
magnitude of the average force exerted on the water by the blade.

10. Robin Hood (m =82 kg) is escaping from a dangerous situation.
With one hand he is gripping the rope that holds up a chandelier
(m =220 kg). When he cuts the rope where it is tied to the floor, the
chandelier will fall, and he will be pulled up to the balcony. Find:
the acceleration with which Robin is pulled upward
the tension in the rope while Robin escapes.

11. What is the net force
acting on the mule?
What is the approximate
answer you expect to get?
Begin by calculating the
components of each force.

13. A 3.0 kg mass hangs at one end of a rope that is attached to a support on a railroad car. When the car accelerates to the right, the rope makes an angle of 4.0° with the vertical.  Find the acceleration of the car.

14. In the vertical direction
In the horizontal direction

15. A block S (the sliding block) has a mass M = 3.3 kg. The block is
free to move along a horizontal frictionless surface and is
connected by a cord that wraps over a frictionless pulley to a
second block H (the hanging block), with mass m = 2.1 kg. The
cord and pulley are “massless”. The hanging block H falls as the
sliding block S accelerates to the right.

16. An inclined plane making an angle of 25o with the horizontal has a
pulley at its top. A 30 kg block on the plane is connected to a freely
hanging 20 kg block by means of a cord passing over the pulley.
Compute the distance that the 20 kg block will fall in 2.0 seconds
starting from rest. Neglect friction.
We now cut the cord. As the block then slides down the inclined
plane, does it accelerate? If so, what is its acceleration?

17. Positive direction is down the inclined plane
                                  
Positive direction is down the inclined plane

18. What is the tension T2 Given: M1 = 12.0 kg M2 = 24.0 kg M3 = 31.0 kg
T3 = 65.0 N
What is the tension T2