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Free body diagrams are used to gain an understanding of the forces (or sometimes the fields) acting on an object. This is a good first step when solving problems involving two or more forces, or forces that are not in line with the motion of an object.

To draw a free body diagram show the relative magnitude and direction of all forces acting on a body:

1. Draw a dot to represent the center of gravity of the object.
2. Draw and label arrows extending outward from the dot to represent the forces acting on the object. Drawing the arrows at least approximately to scale and correct angles helps.
3. Draw a reference frame (x and y axes) with the motion along one of the axes.
4. Dotted lines are drawn along x and y directions to represent the orthogonal components of the forces if necessary.

The relative lengths of the arrows in the diagram imply the direction of net force (and therefore, acceleration). If the acceleration of the object is zero, all forces cancel; if the object is accelerating, the net force is in the direction of the acceleration.

Commonly used forces in free body diagrams are weight (F_g), friction including air resistance (F_f), normal force supplied by a surface (F_N), and applied force (F_a).

Components of forces are often labeled (F_x) or (F_y).

Questions

1. Draw a free body diagram of a parachutist who

a. has just stepped out of the airplane, and is accelerating toward the ground.

b. has opened her parachute and is traveling downward with constant velocity.

2. Draw a free body diagram of a brick

a. at rest on a table.

b. being pushed with constant velocity along a rough horizontal surface.

c. being pushed and speeding up along a rough horizontal surface.

d. sliding freely along a rough horizontal surface and slowing down.

3. Draw a free body diagram of a brick on a rough sloped surface and

a. at rest.

b. accelerating down the slope.

4. A 2.8-kg book resting on a surface inclined at 32º above the horizontal. Find the normal force exerted on the book.

5. A surfer "hangs ten" and accelerates down the sloping face of a wave. If the surfer's acceleration is 3.38 m/s/s and friction can be ignored, what is the angle at which the face of the wave is inclined above the horizontal?

6. A crate is resting on a ramp that is inclined at an angle above the horizontal. As is increased, the crate remains in place until reaches a value of 32.7°. Then the crate begins to slide down the slope.

a. Determine the coefficient of static friction between the crate and the ramp surface.

b. The coefficient of kinetic friction between the crate and the ramp is 0.330. Find the acceleration of the moving crate.

7. A 1.0 kg ball hangs from the ceiling of a truck by a 1.0 m-long string. The truck, whose wheels are in contact with the earth, is accelerating in its forward direction. Draw well-separated free-body diagrams of the ball, and the string. In these diagrams, draw arrows to indicate the approximate relative magnitudes of the forces. Indicate (through table to the free-body diagrams) the pairs of forces related by Newton's 3rd law (3rd law pairs).

8. When a 250 kg crate is on a 25 degree incline, its acceleration is 0.70 m/s/s. What should the incline be for the crate to slide down at a constant speed, where g = 9.81 m/s/s?

9. Vladimir Kurlovich, from Belarus, set the record as the world\'s strongest weightlifter. He did this by lifting and holding above his head a barbell whose mass was 253 kg. Kurlovich\'s mass at the time was roughly 133kg. draw a free body diagram showing the various forces in the problem. Calculate the normal force exerted on each of Kurlovich's feet during the time he was holding the record weight.

Answers

1. a. b.

2. a. b. c.

d.

For solutions to all the problems on this page click here.