# Equilibrium

## Problems

### practice

- A 100 N sign is to be suspended by two cables. Determine the tension in each cable for the given angles…
- 090°, 090°

- 180°, 045°

- 120°, 030°

- Three forces act on a point: 3 N at 0°, 4 N at 90°, and 5 N at 217°.
- What is the net force?
- What fourth force will put the point in equilibrium?

- A 100 kg wooden crate rests on a wooden ramp with an adjustable angle of inclination.
- Draw a free body diagram of the crate.
- If the angle of the ramp is set to 10°, determine…
- the component of the crate's weight that is perpendicular to the ramp
- the component of the crate's weight that is parallel to the ramp
- the normal force between the crate and the ramp
- the static friction force between the crate and the ramp

- At what angle will the crate just begin to slip?

- Write something completely different.

### numerical drill

- Drill
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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

- 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
- Draw a free body diagram of the sled.
- Determine the horizontal component of the tension.
- Determine the vertical component of the tension.
- Determine the kinetic friction force of the snow on the sled.
- Determine the normal force of the snow on the sled.
- Determine the coefficient of kinetic friction between the snow and the sled.

- 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
- Draw a free body diagram of the lawn mower.
- Determine the horizontal component of the homeowner's pushing force.
- Determine the vertical component of the homeowner's pushing force.
- Determine the magnitude of the homeowner's resultant pushing force.
- Determine the weight of the lawn mower.
- Determine the normal force of the ground on the lawn mower.

- 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.
- Draw a free body diagram of the wagon.
- Determine…
- the components of the wagon's weight that are parallel and perpendicular to the ramp
- the normal force of the ramp on the wagon
- the force of friction on the wagon
- the force the child applies to the wagon

- 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.- Draw a free body diagram of the pendulum bob.
- Determine…
- the weight of the bob
- the tension in the string
- the force applied by the student

- 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.- Draw a free body diagram of the pendulum bob.
- Determine…
- the weight of the bob
- the tension in the string
- the force applied by the student

### algebraic

- 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.- Make a free body diagram showing all the forces acting on the head of the broom.
- Find the coefficient of kinetic friction on the broom in terms of the variables
*m*,*g*,*F*, and θ.

- 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.- Draw a free body diagram of the bird.
- Derive an equation for the magnitude of the tension
*T*in the string in terms of*m*,*g*, and θ. - What is the tension in the string when…
- the two halves of the string are vertical (θ = 90°)?
- the two halves of the string are horizontal (θ = 0°)?