Work, Energy, and Power

Suppose a cart has a kinetic energy of 0.5 J. If you add enough mass to double the mass and make the cart go three times as fast, its kinetic energy is now ---.

• 6 J

• 3 J

• 18 J

• 9 J

Answer explanation

KE = ½mv²

Rule of ones:

2 in for m, 3 in for v, 1 in for 1/2

1·2·3² = 18×

18×0.5 = 9 J

Tags

NGSS.MS-PS3-1

NGSS.MS-PS3-4

NGSS.MS-PS3-5

Two equal mass marbles are at the top of a ramp. One marble falls to the ground off the back while the other rolls down the ramp. What is true about the marbles when they reach the ground?

• The marble that rolled down the ramp is moving faster than the marble that fell.

• The marble that fell down the back of the ramp is moving faster than the marble that rolled.

• The marble that rolled down the ramp is not moving when it reaches the ground.

• The two marbles are moving with the same speed.

Answer explanation

They both started off with equal potential energy.

They both wound up with zero potential energy.

They both would have converted the same amount of potential energy into kinetic energy.

They both would have the same speed for the same kinetic energy.

Tags

NGSS.HS-PS2-1

A crane lifts an 8-m long steel girder weighing 2600 N up 15 m off the ground. The crane did ___ of work.

• 0 J

• 39000 J

• 20800 J

• 2600 J

Answer explanation

Force and displacement are in the same direction:

W = F·d

A crane carries an 8-m long steel girder weighing 2600 N out 12 m to the end of the crane. The crane did ___ of work.

• 0 J

• 2600 J

• 20800 J

• 31200 J

Answer explanation

Force and displacement are perpendicular to each other:

W = 0

Potential energy is associated with ---.

• speed

• position

• direction

• temperature

Tags

NGSS.MS-PS3-2

Kinetic energy is associated with ---.

• speed

• position

• direction

• temperature

Tags

NGSS.MS-PS3-1

A block starts at rest at point P at the top of a ramp which is height h above the ground. The block slides down one side and up the other, stopping at a point less than h above the ground.

• The block did not go as high on the other side because gravity pulls down.

• The block did not go as high on the other side because potential energy always has to decrease.

• The block did not go as high on the other side because work from friction made the mechanical energy less.

• The situation as described is impossible to happen.

Answer explanation

The block starts with some potential energy, and no kinetic energy.

The block winds up with less potential energy, and no kinetic energy.

The energy of the system changed; there was a negative change in the energy.

The change in energy of a system is the work done on the system by external forces.

Negative work must have been done by friction or drag or other non-conservative forces.

Tags

NGSS.HS-PS2-1

NGSS.HS-PS3-1

If there is no friction on this track, at which point would the coaster have the most kinetic energy?

• A

• B

• C

• D

Answer explanation

Potential energy can turn into kinetic energy, and kinetic energy can turn into potential energy.

The point with the most kinetic energy would be the point with the least potential energy.

The point with the least potential energy would be the lowest point.

Tags

NGSS.MS-PS3-1

NGSS.MS-PS3-5

Where is the roller coaster gaining potential energy?

• A to B

• B to C

• C to D

• The roller coaster is always losing potential energy

Answer explanation

PE = mgh

Tags

NGSS.MS-PS3-2

A 40-kg person is climbing 3 m up a flight of stairs in 6 seconds. How much work did they do climbing the stairs?

• 400 J

• 1200 J

• 200 J

• 120 J

Answer explanation

W = F·d

The force is the force of gravity:

F = mg

(Use 10 m/s² for g if you're in a hurry)