Answer:
a) a = 0.477 m/s^2
b) u = 0.04862
Explanation:
Given:-
- The rotational speed of the turntable N = 33 rev/min
- The watermelon seed is r = 4.0 cm away from axis of rotation.
Find:-
(a) Calculate the acceleration of the seed, assuming that it does not slip. (b) What is the minimum value of the coefficient of static friction between the seed and the turntable if the seed is not to slip
Solution:-
- First determine the angular speed (w) of the turntable.
w = 2π*N / 60
w = 2π*33 / 60
w = 3.456 rad/s
- The watermelon seed undergoes a centripetal acceleration ( α ) defined by:
α = w^2 * r
α = 3.456^2 * 0.04
α = 0.477 m / s^2
- The minimum friction force (Ff) is proportional to the contact force of the seed.
- The weight (W) of the seed with mass m acts downwards. The contact force (N) can be determined from static condition of seed in vertical direction.
N - W = 0
N = W = m*g
- The friction force of the (Ff) is directed towards the center of axis of rotation, while the centripetal force acts in opposite direction. The frictional force Ff = u*N = u*m*g must be enough to match the centripetal force exerted by the turntable on the seed.
Ff = m*a
u*m*g = m*a
u = a / g
u = 0.477 / 9.81
u = 0.04862
For #2.
(A) The resultant velocity of the boat is the hypotenuse of a right triangle with the sides being the river and boat velocities.
The Pythagorean theorem: h^2 = a^2 + b^2
then you can use: soh cah toa to find any angles.
(B) The river velocity is not opposing the direction of travel, it increases the boats velocity from 2m/s to 2.5m/s
Answer:
V₂ = -22 V
Explanation:
Electric potential and field are related
ΔV = - E d
where ΔV is the potential difference between the plates, E the electric field and d the separation between the plates
In this exercise we are given the parcionero d = 4 mm = 0.004 m, the potential of one of the plates V1 = -6V and the value of the electric field E = 4000 V / m
V₂- V₁ = - E d
V₂ = - Ed + V₁
V₂ = - 4000 0.004 + (- 6)
V₂ = -16 - 6
V₂ = -22 V
Answer:
Linear and rotational Kinetic Energy + Gravitational potential energy
Explanation:
The ball rolls off a tall roof and starts falling.
Let us first consider the potential energy or more specifically gravitational potential energy (
; 
= mass of the ball, 
= acceleration due to gravity, 
= height of the roof). This energy comes because someone or something had to do work to take the ball to the top of the roof against the force of gravity. The potential energy is naturally maximum at the top and minimum when the ball finally reaches the ground.
Now, the ball starts to roll and falls off the roof. It shall continue rotating because of inertia (Newton's first law). This contributes to the rotational kinetic energy (
; 
=moment of inertia of the ball & 
= angular velocity).
Finally comes the linear kinetic energy or simply, kinetic energy (
) which is caused due to the velocity 
of the ball.
Answer:
Explanation:
Generally the workdone in moving the proton is mathematically represented as
Where 
So
Here 
is the velocity at A with value 50 m/s
So
Also
Here is the velocity at A with value 
=> 
=> 
So
Now this workdone is also mathematically represented as
So
Here 
So
Generally proton movement is in the direction of the electric field it means that 
So
