1. Calculate the density of a 5.00 g marble which, when placed in a graduated cylinder containing 60 milliliters of water, raised the volume of
the water to 68 milliliters.
2. An elevator with a mass of 1000kg is lifted 20 meters. How much work
was done on the elevator?
3. Calculate the potential energy of a 12 kg cat at the top of a 42 meter-
high hill.
4. Calculate the kinetic energy in joules of a 1500 kg car that is moving at a
speed of 10 m/s.

1. 0.625 g/mL

2. 2×10⁵ J

3. 5040 J

4. 75000 J

Explanation:

1. Determination of the density.

We'll begin by calculating the volume of the marble. This can be obtained as follow:

Volume of water = 60 mL

Volume of water + Marble = 68 mL

Volume of marble =?

Volume of marble = (Volume of water + Marble) – (Volume of water)

Volume of marble = 68 – 60

Volume of marble = 8 mL

Finally, we shall determine the density of the marble. This can be obtained as follow:

Mass of marble = 5 g

Volume of marble = 8 mL

Density of marble =?

Density = mass / volume

Density of marble = 5 / 8

Density of marble = 0.625 g/mL

2. Determination of the work done.

Mass (m) = 1000 Kg

Height (h) = 20 m

Acceleration due to gravity (g) = 10 m/s²

Workdone (Wd) =?

The work done can be obtained as follow:

Wd = mgh

Wd = 1000 × 10 × 20

Wd= 2×10⁵ J

3. Determination of the potential energy.

Mass (m) = 12 Kg

Height (h) = 42 m

Acceleration due to gravity (g) = 10 m/s²

Potential energy (PE) =?

The potential energy can be obtained as follow:

PE = mgh

PE = 12 × 10 × 42

PE = 5040 J

4. Determination of the kinetic energy.

Mass (m) = 1500 Kg

Velocity (v) = 10 m/s

Kinetic energy (KE) =?

The kinetic energy can be obtained as follow:

KE = ½mv²

KE = ½ × 1500 × 10²

KE = 750 × 100

KE = 75000 J

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