Question 1

A beetle (black dot on the top view shown below) sits on a rapidly rotating turntable. The table rotates faster and faster, and eventually the beetle loses its grip. What is its subsequent trajectory relative to the ground (assuming it cannot fly)?

A) A
B) B
C) B
D) D
E) E
F) F

Accepted Answer

The answer of A beetle (black dot on the top...

Question 2

A cork floats in an inverted jar sitting on a cart, as shown in the left diagram below. If we suddenly accelerate the cart to the right (as shown in the right diagram) what will the cork do:

Accepted Answer

When the cart accelerates to the right, the water inside will be pushed to the back of the jar due to inertia. This creates a slope in the water's surface, higher at the back and lower at the front. The cork, floating on the water, will lean forward towards the lower part of the slope, aligning with the water's surface.

Question 3

When is an elevator a reasonably good inertial reference frame?

Accepted Answer

An elevator acts as a reasonably good inertial reference frame when it is moving at a constant velocity, meaning it is not accelerating or decelerating. This is because, in such a state, the laws of motion inside the elevator are similar to those in a non-accelerating, inertial frame of reference. When the elevator changes speed, it introduces acceleration, making it a non-inertial reference frame where additional fictitious forces appear to act.

Question 4

According to Newton, is a freely falling elevator an accurate inertial reference frame?

Accepted Answer

The answer of According to Newton, is a freely falling...

Question 5

According to Einstein, is a frame at rest on the earth's surface a reasonably accurate inertial frame (ignoring the earth's rotation)?

Accepted Answer

A frame at rest on the Earth's surface is not an inertial frame because it is accelerating upward due to the Earth's gravitational pull. According to Einstein's general theory of relativity, this acceleration is equivalent to a gravitational field, which means that a frame at rest on Earth is not in free fall and thus not an inertial frame.

Question 6

Centrifugal forces are

Accepted Answer

Centrifugal forces are considered fictitious because they arise from the inertia of mass when in a non-inertial (rotating) reference frame, rather than from any physical interaction with another object.

Question 7

You are driving $5 \mathrm{ft}$ or so behind a pickup truck (don't actually try such a stupid tailgating stunt, of course!). A jostled crate tips off the back of the truck with only a very small backward velocity. The crate will not hit your car until after it hits the road, regardless of your speed.

Accepted Answer

When the crate falls off the truck, it initially shares the forward velocity of the truck. Due to inertia, it continues moving forward as it falls. Your car, moving at a similar speed, will not reach the point where the crate lands until after the crate has already hit the road, because both the crate and your car are moving forward at similar speeds.

Question 8

A person standing in the cabin of a jet plane drops a coin. This coin hits the floor of the cabin at a point directly below where it was dropped (as seen in the cabin) no matter how fast the plane is moving.

Accepted Answer

Both the coin and the plane (including its cabin) are moving at the same velocity. When the coin is dropped, it retains the forward velocity of the plane, ensuring it falls straight down relative to the cabin.

Question 9

A tennis ball is dropped from rest at the exact same instant and height that a bullet is fired horizontally. Which hits the ground first (ignoring air resistance)?

Accepted Answer

Both the tennis ball and the bullet are subject to the same gravitational acceleration, and since they start from the same height, they will hit the ground at the same time, assuming air resistance is ignored. Horizontal motion does not affect the time it takes for an object to fall to the ground.

Question 10

As a projectile moves along its parabolic trajectory, which of the following remain constant (ignoring air resistance, and defining the $z$ axis as pointing upward)?

Accepted Answer

The answer of As a projectile moves along its parabolic...

Question 11

Suppose we throw a baseball with an initial speed of $12 \mathrm{~m} / \mathrm{s}$ in a direction $60^{\circ}$ upward from the horizontal. What is the baseball's speed at the peak of its trajectory? (Hint: You do not need to do a lot of calculating here.)

Accepted Answer

At the peak of its trajectory, the vertical component of the baseball's velocity is 0 m/s due to gravity, but the horizontal component remains unchanged. The initial speed of 12 m/s at a $60^{\circ}$ angle means the horizontal component is $12 \cos(60^{\circ}) = 6 \mathrm{~m} / \mathrm{s}$, which is the speed at the peak.

Question 12

Imagine you serve a tennis ball with an initial speed of $10 \mathrm{~m} / \mathrm{s}$ in a direction $10^{\circ}$ below the horizontal. What is its speed at the peak of its trajectory?

Accepted Answer

Since the ball is served below the horizontal, it does not have an upward trajectory and thus does not reach a peak.

Question 13

An orbiting satellite experiences no forces other than the force of gravity. It therefore exhibits simple projectile motion.

Accepted Answer

An orbiting satellite is indeed primarily influenced by the force of gravity, but its motion is not considered simple projectile motion. Simple projectile motion occurs under the influence of gravity in a uniform, two-dimensional plane close to the Earth's surface, where the only force acting after the initial launch is gravity, assuming air resistance is negligible. In contrast, an orbiting satellite follows a curved path around the Earth due to the constant gravitational pull, which keeps changing its direction without changing its speed, resulting in circular or elliptical orbits, not the parabolic trajectory seen in simple projectile motion.

Question 14

Imagine you throw a tennis ball vertically into the air. At the exact top of its trajectory it is at rest. What is the magnitude of its acceleration at this point?

Accepted Answer

At the top of its trajectory, the velocity of the tennis ball is 0 m/s, but it is still accelerating due to gravity at $9.8 \mathrm{~m} / \mathrm{s}^{2}$ downwards. The magnitude of acceleration does not depend on the direction, hence the answer is $9.8 \mathrm{~m} / \mathrm{s}^{2}$.

Question 15

Two balls have the same size and surface texture, but one is twice as heavy as the other. How many times larger is the terminal speed of the more massive ball falling through air than that of the lighter ball?

Accepted Answer

The terminal speed $v_t$ is proportional to the square root of the mass ($m$) when other factors like size and drag coefficient are constant. Therefore, if one ball is twice as heavy, its terminal speed will be $\sqrt{2}$ times larger.

Question 16

Two balls have the same weight and surface texture, but one has twice the diameter of the other. How many times larger is the terminal speed of the smaller ball falling through air than that of the bigger ball?

Accepted Answer

The answer of Two balls have the same weight and...

Question 17

Suppose a baseball travels $425 \mathrm{ft}(130 \mathrm{~m})$ from where the batter hits it to where it lands in the stands. The ball's velocity makes an angle of $40^{\circ}$ with respect to the horizontal as the ball leaves the bat. Suppose we first calculate the ball's initial speed ignoring drag and find it to be $\left|\vec{v}_{0}\right|$. Including drag might plausibly require a higher initial speed for the ball to travel the same horizontal distance. On the other hand, by slowing down the ball's vertical motion, including drag will increase the ball's flight time, allowing the ball the same distance with a slower horizontal velocity. So if we include drag, for the ball to fly the same horizontal distance will we need

Accepted Answer

DIncluding drag affects the ball's trajectory by slowing it down, which complicates the prediction of whether a greater or lesser initial speed is needed without specific details about the drag's characteristics. Additionally, drag can both decelerate the ball and potentially alter its flight path, necessitating more information for a definitive answer.

Question 18

If you double the amplitude of a harmonic oscillator, the oscillator's period

Accepted Answer

The period of a harmonic oscillator is independent of its amplitude. It depends only on the mass and the spring constant (or other equivalent parameters in different types of oscillators).

Question 19

If you double the amplitude of a harmonic oscillator, the object's maximum speed does what?

Accepted Answer

The maximum speed of a harmonic oscillator is directly proportional to its amplitude. Doubling the amplitude doubles the maximum speed.

Question 20

If you double the spring constant of a harmonic oscillator, the oscillation frequency does what?

Accepted Answer

The oscillation frequency of a harmonic oscillator is given by $f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$, where $k$ is the spring constant and $m$ is the mass. Doubling $k$ results in the square root of 2 increase in the frequency, since $f' = \frac{1}{2\pi}\sqrt{\frac{2k}{m}} = \sqrt{2} \cdot \frac{1}{2\pi}\sqrt{\frac{k}{m}} = \sqrt{2} \cdot f$.

Quiz 2: The Laws of Physics Are Universal Newtonian Mechanics

A beetle (black dot on the top view shown below) sits on a rapidly rotating turntable. The table rotates faster and faster, and eventually the beetle loses its grip. What is its subsequent trajectory relative to the ground (assuming it cannot fly)? A) A B) B C) B D) D E) E F) F

A cork floats in an inverted jar sitting on a cart, as shown in the left diagram below. If we suddenly accelerate the cart to the right (as shown in the right diagram) what will the cork do:

When is an elevator a reasonably good inertial reference frame?

According to Newton, is a freely falling elevator an accurate inertial reference frame?

According to Einstein, is a frame at rest on the earth's surface a reasonably accurate inertial frame (ignoring the earth's rotation) ?

Centrifugal forces are

A person standing in the cabin of a jet plane drops a coin. This coin hits the floor of the cabin at a point directly below where it was dropped (as seen in the cabin) no matter how fast the plane is moving.

A tennis ball is dropped from rest at the exact same instant and height that a bullet is fired horizontally. Which hits the ground first (ignoring air resistance) ?

As a projectile moves along its parabolic trajectory, which of the following remain constant (ignoring air resistance, and defining the $z$ axis as pointing upward) ?

Suppose we throw a baseball with an initial speed of $12 \mathrm{~m} / \mathrm{s}$ in a direction $60^{\circ}$ upward from the horizontal. What is the baseball's speed at the peak of its trajectory? (Hint: You do not need to do a lot of calculating here.)

Imagine you serve a tennis ball with an initial speed of $10 \mathrm{~m} / \mathrm{s}$ in a direction $10^{\circ}$ below the horizontal. What is its speed at the peak of its trajectory?

An orbiting satellite experiences no forces other than the force of gravity. It therefore exhibits simple projectile motion.

Imagine you throw a tennis ball vertically into the air. At the exact top of its trajectory it is at rest. What is the magnitude of its acceleration at this point?

Two balls have the same size and surface texture, but one is twice as heavy as the other. How many times larger is the terminal speed of the more massive ball falling through air than that of the lighter ball?

Two balls have the same weight and surface texture, but one has twice the diameter of the other. How many times larger is the terminal speed of the smaller ball falling through air than that of the bigger ball?

If you double the amplitude of a harmonic oscillator, the oscillator's period

If you double the amplitude of a harmonic oscillator, the object's maximum speed does what?

If you double the spring constant of a harmonic oscillator, the oscillation frequency does what?

Quiz 2: The Laws of Physics Are Universal Newtonian Mechanics

A beetle (black dot on the top view shown below) sits on a rapidly rotating turntable. The table rotates faster and faster, and eventually the beetle loses its grip. What is its subsequent trajectory relative to the ground (assuming it cannot fly)? A) A B) B C) B D) D E) E F) F

A cork floats in an inverted jar sitting on a cart, as shown in the left diagram below. If we suddenly accelerate the cart to the right (as shown in the right diagram) what will the cork do:

When is an elevator a reasonably good inertial reference frame?

According to Newton, is a freely falling elevator an accurate inertial reference frame?

According to Einstein, is a frame at rest on the earth's surface a reasonably accurate inertial frame (ignoring the earth's rotation) ?

Centrifugal forces are

A person standing in the cabin of a jet plane drops a coin. This coin hits the floor of the cabin at a point directly below where it was dropped (as seen in the cabin) no matter how fast the plane is moving.

A tennis ball is dropped from rest at the exact same instant and height that a bullet is fired horizontally. Which hits the ground first (ignoring air resistance) ?

As a projectile moves along its parabolic trajectory, which of the following remain constant (ignoring air resistance, and defining the zzz axis as pointing upward) ?

Suppose we throw a baseball with an initial speed of 12 m/s12 \mathrm{~m} / \mathrm{s}12 m/s in a direction 60∘60^{\circ}60∘ upward from the horizontal. What is the baseball's speed at the peak of its trajectory? (Hint: You do not need to do a lot of calculating here.)

Imagine you serve a tennis ball with an initial speed of 10 m/s10 \mathrm{~m} / \mathrm{s}10 m/s in a direction 10∘10^{\circ}10∘ below the horizontal. What is its speed at the peak of its trajectory?

An orbiting satellite experiences no forces other than the force of gravity. It therefore exhibits simple projectile motion.

Imagine you throw a tennis ball vertically into the air. At the exact top of its trajectory it is at rest. What is the magnitude of its acceleration at this point?

Two balls have the same size and surface texture, but one is twice as heavy as the other. How many times larger is the terminal speed of the more massive ball falling through air than that of the lighter ball?

Two balls have the same weight and surface texture, but one has twice the diameter of the other. How many times larger is the terminal speed of the smaller ball falling through air than that of the bigger ball?

If you double the amplitude of a harmonic oscillator, the oscillator's period

If you double the amplitude of a harmonic oscillator, the object's maximum speed does what?

If you double the spring constant of a harmonic oscillator, the oscillation frequency does what?

As a projectile moves along its parabolic trajectory, which of the following remain constant (ignoring air resistance, and defining the $z$ axis as pointing upward) ?

Suppose we throw a baseball with an initial speed of $12 \mathrm{~m} / \mathrm{s}$ in a direction $60^{\circ}$ upward from the horizontal. What is the baseball's speed at the peak of its trajectory? (Hint: You do not need to do a lot of calculating here.)

Imagine you serve a tennis ball with an initial speed of $10 \mathrm{~m} / \mathrm{s}$ in a direction $10^{\circ}$ below the horizontal. What is its speed at the peak of its trajectory?