Concept MC Questions - Clarifying Earth's Rotation & Ladder Friction in Space

[bobby13]

Hi, I have some review multiple choice questions, and some of them, I can't understand why the answer is so. If you could clarify the concepts, that'd be great!

Which statement best describes the Earth’s rotation about its
axis?
a)The tangential velocity is the same at all points on the Earth’s
surface.
b)The angular velocity is greatest at the Earth’s equator.
c)The angular acceleration is zero at all points on the Earth’s
surface.
d)The centripetal acceleration of a point on the Earth’s surface
is zero.

The answer is C. For this one, I didnt even know where to begin. I only could eliminate D because since it is rotating, it has to have a centripetal acceleration.


A ladder leans against a frictionless wall, but is prevented from
falling because of friction between it and the ground. If you
shift the base of the ladder toward the wall,
a) The normal force on the ladder from the ground decreases.
b) The static frictional force on the ladder from the ground
decreases.
c) The normal force on the ladder from the wall increases.
d) The maximum static frictional force on the ladder from the
ground increases.
e) None of the above.

The answer is B. I thought the answer was E because the normal force is the same, and the cofficient of static friction is the same, then the force of static friction should be the same.


Two astronauts (both 70 kg) are floating motionless in empty
space far from the Earth. One of them is holding a 20-kg
oxygen tank. He pushes the tank directly toward the second
astronaut, who catches and holds it. If the speed of the tank
relative to the second astronaut was 2.0 m/sec, then the final
speed of the second astronaut relative to the first one (after the
second one has caught the tank) is:
(A) 0.4 m/sec
(B) 0.6 m/s
(C) 1.0 m/s
(D) 1.5 m/s

Answer is C. I am really not too sure where to being here


Thanks in advance

 

[Chi Meson]

First question: look up the definition of angular acceleration. read it aloud. Think to yourself, which part of the Earth completes one rotation in a shorter time than other parts of the earth?

 

[quicknote]

for your help!

Hello, thank you for reaching out. I am happy to clarify these concepts for you.

For the first question, the Earth's rotation about its axis is a complex motion involving both tangential and angular velocity. The tangential velocity is the linear velocity of a point on the Earth's surface as it rotates, and it is the same at all points on the surface. This means that a point on the equator, for example, is moving faster than a point near the poles. However, the angular velocity, which is the rate of change of the angle of rotation, is greatest at the Earth's equator. This is because the equator is farther from the axis of rotation and has a larger circumference to cover in the same amount of time. The correct answer, as you stated, is C because the angular acceleration, which is the rate of change of the angular velocity, is zero at all points on the Earth's surface. This is because the Earth's rotation is constant and does not change in speed.

For the second question, if the base of the ladder is shifted towards the wall, the normal force on the ladder from the ground will decrease because the ladder is now closer to the wall and the weight of the ladder is distributed more towards the wall. This means that the static frictional force, which is dependent on the normal force, will also decrease. The correct answer is B.

For the third question, we can use the concept of conservation of momentum to solve it. The initial momentum of the system (two astronauts and the tank) is zero since they are all motionless. When the first astronaut pushes the tank towards the second one, the tank gains momentum and the astronaut loses the same amount of momentum. This means that the final momentum of the system must also be zero. We can use the equation p = mv to calculate the final speed of the second astronaut. The mass of the second astronaut is 70 kg and the mass of the tank is 20 kg, so the total mass of the system after the tank is caught is 90 kg. The initial momentum of the tank is 20 kg x 2 m/s = 40 kg m/s. This means that the final momentum of the second astronaut must be -40 kg m/s to balance out the system. Using the equation p = mv again, we can solve for the final velocity of the second astronaut, which is -40 kg m/s divided by 90 kg,