The Physics
Hypertextbook
Opus in profectus

# Statics

## Problems

### practice

1. A 100 N sign is to be suspended by two cables. Determine the tension in each cable for the given angles…
2. Three forces act on a point: 3 N at 0°, 4 N at 90°, and 5 N at 217°.
1. What is the net force?
2. What fourth force will put the point in equilibrium?
3. A 100 kg wooden crate rests on a wooden ramp with an adjustable angle of inclination.
1. Draw a free body diagram of the crate.
2. If the angle of the ramp is set to 10°, determine…
1. the component of the crate's weight that is perpendicular to the ramp
2. the component of the crate's weight that is parallel to the ramp
3. the normal force between the crate and the ramp
4. the static friction force between the crate and the ramp
3. At what angle will the crate just begin to slip?
4. Write something completely different.

### numerical drill

1. Drill
1. Four forces act on an object: 70 N at 0°, 90 N at 90°, 30 N at 180°, and 60 N at 270°. Find the magnitude and direction of the fifth force that produces equilibrium in the object.
2. Four forces act on an object: 90 N at 0°, 70 N at 90°, 60 N at 180°, and 30 N at 270°. Find the magnitude and direction of the fifth force that produces equilibrium in the object.
3. Three forces act on an object: 32 N at 0°, 55 N at 37°, and 24 N at 90°. Find the magnitude and direction of the fourth force that produces equilibrium in the object.
4. Three forces act on an object: 24 N at 0°, 55 N at 53°, and 32 N at 90°. Find the magnitude and direction of the fourth force that produces equilibrium in the object.
5. Three forces act on an object: 55 N at 37°, 32 N at 180°, and 45 N at 270°. Find the magnitude and direction of the fourth force that produces equilibrium in the object.
6. Three forces act on an object: 55 N at 53°, 45 N at 180°, and 32 N at 270°. Find the magnitude and direction of the fourth force that produces equilibrium in the object.
7. Two forces act on an object: 20 N at 37° and 15 N at 127°. Find the magnitude and direction of the third force that produces equilibrium in the object.
8. Two forces act on an object: 15 N at −37° and 20 N at +53°. Find the magnitude and direction of the third force that produces equilibrium in the object.

### numerical

1. A child is pulling a 30 N sled at a constant velocity with a rope that makes a 37° angle with the horizontal. The tension in the rope is 5.0 N.
1. Draw a free body diagram of the sled.
2. Determine the horizontal component of the tension.
3. Determine the vertical component of the tension.
4. Determine the kinetic friction force of the snow on the sled.
5. Determine the normal force of the snow on the sled.
6. Determine the coefficient of kinetic friction between the snow and the sled.
2. A home owner pushes a 20 kg non-motorized lawn mower at a constant horizontal velocity. Her arms make a 30° angle with the ground. The effective friction force on the lawn mower is 45 N.
1. Draw a free body diagram of the lawn mower.
2. Determine the horizontal component of the homeowner's pushing force.
3. Determine the vertical component of the homeowner's pushing force.
4. Determine the magnitude of the homeowner's resultant pushing force.
5. Determine the weight of the lawn mower.
6. Determine the normal force of the ground on the lawn mower.
3. A child is pushing a 9.5 kg wagon up a 10° ramp at a constant velocity. His arms are parallel to the ramp as he pushes. The effective coefficient of kinetic friction of the bearings against the axle is 0.21.
1. Draw a free body diagram of the wagon.
2. Determine…
1. the components of the wagon's weight that are parallel and perpendicular to the ramp
2. the normal force of the ramp on the wagon
3. the force of friction on the wagon
4. the force the child applies to the wagon
4. A laboratory pendulum is held in place by a student so that the string makes a 30° angle with the vertical. The student exerts a force that is perpendicular to the string. The bob has a mass of 48 g and the string is 33 cm long.
1. Draw a free body diagram of the pendulum bob.
2. Determine…
1. the weight of the bob
2. the tension in the string
3. the force applied by the student
5. A laboratory pendulum is held by a student so that the string makes a 30° angle with the vertical. The student pulls horizontally on the bob so that it stays in place. The bob has a mass of 48 g and the string is 33 cm long.
1. Draw a free body diagram of the pendulum bob.
2. Determine…
1. the weight of the bob
2. the tension in the string
3. the force applied by the student

### algebraic

1. A push broom of mass m is pushed across a horizontal floor at a constant velocity by a force of magnitude F directed at an angle θ with respect to the floor.
1. Make a free body diagram showing all the forces acting on the head of the broom.
2. Find the coefficient of kinetic friction on the broom in terms of the variables m, g, F, and θ.
2. A small bird of mass m perches on the center of a string of negligible mass that is suspended from two ends at equal height. When this happens, the string takes on a "v" shape with the bird at the vertex. The string on either side of the bird makes a small angle θ with the horizontal.
1. Draw a free body diagram of the bird.
2. Derive an equation for the magnitude of the tension T in the string in terms of m, g, and θ.
3. What is the tension in the string when…
1. the two halves of the string are vertical (θ = 90°)?
2. the two halves of the string are horizontal (θ = 0°)?