A small cylinder rests on a circular turntable that is rotating clockwise at a constant speed. Which set of vectors gives the di
rection of the velocity v with arrow, acceleration a with arrow of the cylinder, and the net force ΣF with arrow that acts on it?
(A) 3
(B) 4
(C) 1
(D) 2
(A) 3
(B) 4
(C) 1
(D) 2
1 answer:
The question lacks a diagram. Additionally, the choices should have graphical representations. Consequently, I have included the missing diagram and the vector illustrations below.
Answer:
The correct representation is included below. Force and acceleration will be directed towards the center of rotation, while velocity will be along the tangent to the circular motion. Option (D).
Explanation:
From the figure, we can derive the following conclusions:
1. The cylinder experiences uniform circular motion as the circular table maintains a constant speed.
2. In circular motion, velocity points tangentially to the circular path.
3. Circular motion necessitates centripetal force acting on the object that enables it to travel in a circular path.
4. The centripetal force directs radially inward towards the center.
5. This centripetal force produces a centripetal acceleration acting on the body.
6. According to Newton's second law, the net acceleration of an object aligns with the net force applied on it. Thus, centripetal acceleration also acts radially inward.Therefore, it's clear that at a given moment, velocity will be horizontal while force and acceleration will act vertically downward, as shown in the illustration below. Below is option (D).
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Answer:
The resulting velocity for him will be 0.187 m/s in reverse direction.
Explanation:
Given:
The mass of the man is,
The mass of the ball is,
The initial velocity of the man is,
The initial velocity of the ball is,
The final velocity of the ball is,
The final velocity of the man is,
To determine this scenario, we employ the principle of momentum conservation.
This principle states that the total initial momentum equals the total final momentum.Momentum is calculated by multiplying mass by velocity.
Initial momentum = Initial momentum of the man and the ballInitial momentum =
Final momentum = Final momentum of the man and the ball
Final momentum =
Hence, the total initial momentum equals the total final momentum
The negative sign indicates that the man moves backward.
Thus, his final velocity ends up being 0.187 m/s backward.
Answer:
10000 V
0.00225988700565 m²
Explanation:
E = Electric field =
d = Distance = 2.5 mm
Q = Charge = 80 nC
= Permittivity of free space =
The potential difference is calculated as
The potential difference across the plates amounts to 10000 V
Area is determined by
The area of each plate measures 0.00225988700565 m²
Capacitance is determined by
The capacitance is
The formula for range is:
Given values are:
where θ equals 14.1 degrees
Using the equation above,
The calculated range is 66.7 meters.
Therefore, the range is approximately 66.1 meters.