Motion
A train is moving in a straight line at constant speed. A passenger tosses a coin vertically upwards relative to themselves. Will it land back in their hand, behind it, or in front of it? Explain why.
Back in their hand. The coin retains the train’s horizontal velocity, so the coin and the passenger continue moving horizontally together.
A heavy truck collides with a light car. During the collision, which statement is correct?
A. The truck exerts a greater force on the car.
B. The car exerts a greater force on the truck.
C. The forces are equal in magnitude.
Why can the vehicles have different accelerations?
C. By Newton’s third law, the forces are equal in magnitude and opposite in direction. Since (a=F/m), the lighter car has a greater acceleration magnitude due to this interaction.
A coin lies at the bottom of a container of water. You look at it from the air, almost vertically downwards. Does it appear closer to the surface or deeper than it really is? Explain why.
Closer to the surface. Light refracts away from the normal as it leaves the water. Tracing the emerging rays backwards gives a virtual image above the actual coin.
A converging lens forms a sharp image on a screen. The lower half of the lens is covered with an opaque card. What happens?
A. The upper half of the image disappears.
B. The lower half of the image disappears.
C. The whole image remains, but becomes dimmer.
D. The entire image disappears.
Explain your choice.
C. Light from each point of the object passes through different parts of the lens. The uncovered half can still form the entire image, but less light reaches the screen.
Two balls start at the same height. At the same instant, one is released from rest and the other is thrown horizontally. Which reaches the horizontal floor first? Explain why.
They reach the floor simultaneously. Both have zero initial vertical velocity and the same downward acceleration. Horizontal motion does not affect the time taken to fall.
A person stands on bathroom scales in a lift. The lift is moving upwards but slowing down. Is the scale reading greater than, less than, or equal to the reading when the lift is stationary? Explain why.
Less than the stationary reading. The lift’s acceleration is downwards, so the upward normal force measured by the scales is smaller than the person’s weight:
N=m(g-a),
where (a) is the magnitude of the downward acceleration.
Light passes from air into ordinary glass. What happens to its:
a) frequency;
b) speed;
c) wavelength?
State whether each increases, decreases, or stays the same.
a) Frequency stays the same.
b) Speed decreases.
c) Wavelength decreases.
Where must an object be placed relative to a converging lens to produce an upright, magnified image when viewed through it? Can this image be formed on a screen?
Between the lens and its focal point. The image is upright, magnified and virtual. It cannot be formed directly on a screen because the emerging rays do not actually converge at the image position.
A ball is thrown vertically upwards. At the highest point, what are its velocity and acceleration? Give the magnitude and direction of the acceleration.
Its instantaneous velocity is zero. Its acceleration is (10 m/s^2) downwards. Gravity continues to act even when the ball is momentarily at rest.
You hold a heavy backpack stationary for one minute. Your arms become tired.
How much mechanical work do you do on the backpack during that minute? Why do you still use energy?
You do zero mechanical work on the backpack, because it does not move: work requires displacement.
Your muscles still consume chemical energy to maintain tension, even though the backpack remains stationary.
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A person is 180 cm tall and wants to see their entire body in a vertical plane mirror. What is the minimum mirror height? Would it change if the person moved further away? Assume the mirror is positioned appropriately.
90 cm — half the person’s height. This does not depend on their distance from the mirror. The reflection points needed to see the top of the head and the feet lie halfway in height between the eyes and those respective points.
A student walks the first 100 m at 1 m/s and the next 100 m at 2 m/s. What is their average speed over the entire journey?
A. 1.33 m/s
B. 1.50 m/s
C. 1.67 m/s
Show your reasoning.
approximately 1.33 m/s
Two students stand facing each other on an ice rink, initially at rest. Their masses are 50 kg and 100 kg. They push each other apart.
If the 50 kg student moves away at 2 m/s, what is the velocity of the 100 kg student? Which student has more kinetic energy?
Neglect friction.
The 100 kg student moves at 1 m/s in the opposite direction, by conservation of momentum:
50 × 2 + 100 × v = 0, so v = −1 m/s.
The lighter student has twice as much kinetic energy:
50 kg student: ½ × 50 × 2² = 100 J.
100 kg student: ½ × 100 × 1² = 50 J.
The energy comes from chemical energy in their bodies.
A ray of light enters a rectangular glass block from air at an angle to the normal. It then leaves through the opposite, parallel face into air.
Is the emerging ray parallel to the original incident ray? Does it follow exactly the same line? Explain why.
The emerging ray is parallel to the incident ray, but laterally displaced.
The ray bends towards the normal when entering the glass and away from the normal when leaving. Because the faces are parallel and the surrounding medium is the same, the angle of emergence equals the angle of incidence.
A camera forms a sharp image of a distant mountain on its sensor. It is then pointed at a nearby person.
To focus on the person, should the lens move closer to the sensor or further away? Assume a thin converging lens with a fixed focal length. Explain your answer.
Answer: Further away from the sensor.
For a very distant object, the image forms approximately at the focal plane. As the object moves closer to the lens, its image distance increases, so the lens-to-sensor distance must increase.
From the thin-lens equation:
1/v = 1/f − 1/u.
As the object distance u decreases, the image distance v increases, provided the object remains outside the focal point.