He should cleverly, using charm and subterfuge, entice the dumbbell slowly in the direction of where he had hidden the scale. As long as Hunter isn't obvious about it, the dumbbell will swallow his faux charm, and will remain naively oblivious to his true purpose.
Given that they are all on the same bus that is travelling in a straight line at the same velocity, when Elle throws the ball directly upwards, the ball will simply fall back to her. This is because the bus, Elle, and the ball are all travelling in the same direction and at the same speed. Among the choices, the correct answer is A.
If an icy surface means no friction, then Newton's second law tells us the net forces on either block are
• <em>m</em> = 1 kg:
∑ <em>F</em> (parallel) = <em>mg</em> sin(45°) - <em>T</em> = <em>ma</em> … … … [1]
∑ <em>F</em> (perpendicular) = <em>n</em> - <em>mg</em> cos(45°) = 0
Notice that we're taking down-the-slope to be positive direction parallel to the surface.
• <em>m</em> = 0.4 kg:
∑ <em>F</em> (vertical) = <em>T</em> - <em>mg</em> = <em>ma</em> … … … [2]
<em />
Adding equations [1] and [2] eliminates <em>T</em>, so that
((1 kg) <em>g</em> sin(45°) - <em>T </em>) + (<em>T</em> - (0.4 kg) <em>g</em>) = (1 kg + 0.4 kg) <em>a</em>
(1 kg) <em>g</em> sin(45°) - (0.4 kg) <em>g</em> = (1.4 kg) <em>a</em>
==> <em>a</em> ≈ 2.15 m/s²
The fact that <em>a</em> is positive indicates that the 1-kg block is moving down the slope. We already found the acceleration is <em>a</em> ≈ 2.15 m/s², which means the net force on the block would be ∑ <em>F</em> = <em>ma</em> ≈ (1 kg) (2.15 m/s²) = 2.15 N directed down the slope.
<span>a. The magnitude of the vector is doubled as well.
Let's say we have a 2-dimensional vector with components x and y.
It's magnitude lâ‚ is given by:
lâ‚ = âš(x² + y²)
If we double the components x and y, the new magnitude lâ‚‚ is:
lâ‚‚ = âš((2x)² + (2y²))
With a bit of algebra...
lâ‚‚ = âš(4x² + 4y²)
lâ‚‚ = âš4(x² + y²)
lâ‚‚ = 2âš(x² + y²)
We can write the new magnitude lâ‚‚ in terms of the old magnitude lâ‚.
lâ‚‚ = 2lâ‚
Therefore, the new magnitude is double the old one.
It should be clear that this relationship applies to 3D (and 1D) vectors as well.
b. The direction angle is unchanged.
The direction angle θ₠for a 2-dimensional vector is given by:
θ₠= arctan(y / x)
If we double both components, we get:
θ₂ = arctan(2y / 2x)
θ₂ = arctan(y / x)
θ₂ = θâ‚
The new direction angle is the same as the old one.</span>
Answer:
This is because of the static electricity which is generated in bodies due to friction. Time to time, the door knob gets touched by many people and the charge on it goes on increasing because of increasing friction. When the charge is increased much, after a considerable time, one may get a spark or a mild shock.
