# 35 Unit 4 Review, Practice, and Assessment

### Learner Outcomes

- Compare and contrast mass, volume, density, weight and apparent weight and explain how each are measured.[2]
- Explain how the concept of static equilibrium plays into the measurement of weight and apparent weight. [2]
- Apply Archimedes’ principle and density concepts to predict if objects will sink or float. [2]
- Experimentally determine an object’s mass, weight, volume, and density. [5]

**Outcome 1**

1) Which has greater density between a kilogram of feathers and a kilogram of pennies? Which has greater volume? Which has greater mass?

2) What is the weight in Newtons of a 3 **kg** textbook?

3) (a) Convert your own weight from pounds to Newtons.

(b) Then calculate your mass in kilograms. Show all work.

4) The acceleration due to gravity (*g*) on the moon is 1/6 that on the surface of Earth.

(a) Based on your answers to the previous question, what would your weight be on the moon?

(b) What would your mass be on the moon?

**Outcome 2**

5) For each object below, draw a free body diagram:

a) A car hanging from a crane (there are two forces).

b) A car skidding to a stop (there are three forces).

c) A car with the parking brake set being pushed on by a someone, but not moving (there are four forces here, but two of them are the same type).

6) A person stands on a scale.

a) What type of force is pulling them down?

b) What type of force is provided by the scale to hold them up?

c) Draw a free body diagram of this situation.

7) A 7 **N** force pushes on an object to the right and a 7 **N** force pushes on the object to the left.

(a) What is the net force?

(b) Can the object be in static equilibrium?

8) A 5 **N** force pushes on an object to the right and a 7 **N** force pushes on the object to the left.

(a) What is the net force?

(b) Can the object be in static equilibrium?

9) You push on a large box with 120 **N** of force, but it doesn’t move.

(a) How large is the friction force?

(b) Draw a free body diagram of the situation.

**Outcome 3**

10) You are helping a 48 **lb** toddler learn to float in a swimming pool.

(a) What weight of water must the toddler displace in order to float?

(b) What volume of water must the toddler displace in order to float?

(c) Currently the toddler doesn’t like water to cover his ears and holds his head mostly out of the water. You notice that it feels as though he only weighs 3 **lbs**. Draw a free body diagram of the situation.

(d) How large is the buoyant force on the toddler?

(e) If the toddler were to lower his head fully half-way into the water (past the ears), he would displace another 0.4 gallons** **worth of water**. **Would the toddler float then? [Hint: Water as a weight density of 8.34 **lbs**/**gal**]

11) An object has a volume of 0.5** m ^{3}** and weight of 150

**N**.

(a) What is the maximum volume of water it can displace?

(b) What weight of water can it displace?

(c) Will it float?

(d) Is the object in the previous problem more or less dense than water?

12) Calculate the density of the object referred to in the previous problem.

13) An object has a weight of 5.5 **N** and an apparent weight of 3.5 **N** when fully submerged.

(a) Will the object float?

(b) Calculate the density of the object.

relation between the amount of a material and the space it takes up, calculated as mass divided by volume.

a quantity of space, such as the volume within a box or the volume taken up by an object.

a measurement of the amount of matter in an object made by determining its resistance to changes in motion (inertial mass) or the force of gravity applied to it by another known mass from a known distance (gravitational mass). The gravitational mass and an inertial mass appear equal.

the force of gravity on on object, typically in reference to the force of gravity caused by Earth or another celestial body

the rate at which an object changes velocity when gravity is the only force acting on the object

a graphical illustration used to visualize the forces applied to an object

any interaction that causes objects with mass to change speed and/or direction of motion, except when balanced by other forces. We experience forces as pushes and pulls.

the total amount of remaining unbalanced force on an object

the state being in equilibrium (no unbalanced forces or torques) and also having no motion

a force that acts on surfaces in opposition to sliding motion between the surfaces

the upward force exerted by any fluid upon a body placed in it

the reading on a scale that is used to measure the weight of an object that is submerged in a fluid