4. Consider a 1 kg block is on a 45° slope of ice. It is connected to a 0.4 kg block by a cable and pulley. Does the 1 kg block move or down the slope? What is the net force on it and
its acceleration? (8 pts)

If an icy surface means no friction, then Newton's second law tells us the net forces on either block are

• m = 1 kg:

∑ F (parallel) = mg sin(45°) - T = ma … … … [1]

∑ F (perpendicular) = n - mg cos(45°) = 0

Notice that we're taking down-the-slope to be positive direction parallel to the surface.

• m = 0.4 kg:

∑ F (vertical) = T - mg = ma … … … [2]

Adding equations [1] and [2] eliminates T, so that

((1 kg) g sin(45°) - T ) + (T - (0.4 kg) g) = (1 kg + 0.4 kg) a

(1 kg) g sin(45°) - (0.4 kg) g = (1.4 kg) a

==>   a ≈ 2.15 m/s²

The fact that a is positive indicates that the 1-kg block is moving down the slope. We already found the acceleration is a ≈ 2.15 m/s², which means the net force on the block would be ∑ F = ma ≈ (1 kg) (2.15 m/s²) = 2.15 N directed down the slope.

are there answer choices to this question? this seems like a question where you have options to choose from.

another example of kinetic energy would be,

kinetic energy   >     moving energy

answer   >   letter choice (c),   a hammer falling off a table.

hope that !                                         : )