Answer:
The value is
Explanation:
From the question we are that
The velocity 
The time taken is
The total mass of the train is 
Generally the average power delivered is mathematically represented as
=>
=>
Answer:
5 N
Explanation:
The bucket is moving at a constant speed of 2m/s Therefore F=ma is 0 N for this to be correct the magnitude of the force exerted by the rope must be equal to the weight of the bucket which is 5 N
Answer:

Explanation:
To solve this problem we use the formula for accelerated motion:

We will take the initial position as our reference (
) and the downward direction as positive. Since the rock departs from rest we have:

Which means our acceleration would be:

Using our values:

Answer:
The height is 
A circular hoop of different diameter cannot be released from a height 30cm and match the sphere speed because from the conservation relation the speed of the hoop is independent of the radius (Hence also the diameter )
Explanation:
From the question we are told that
The height is 
The angle of the slope is 
According to the law of conservation of energy
The potential energy of the sphere at the top of the slope = Rotational kinetic energy + the linear kinetic energy

Where I is the moment of inertia which is mathematically represented as this for a sphere

The angular velocity
is mathematically represented as

So the equation for conservation of energy becomes
![mgh_s = \frac{1}{2} [\frac{2}{5} mr^2 ][\frac{v}{r} ]^2 + \frac{1}{2}mv^2](https://tex.z-dn.net/?f=mgh_s%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5B%5Cfrac%7B2%7D%7B5%7D%20mr%5E2%20%5D%5B%5Cfrac%7Bv%7D%7Br%7D%20%5D%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
![mgh_s = \frac{1}{2} mv^2 [\frac{2}{5} +1 ]](https://tex.z-dn.net/?f=mgh_s%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2%20%5B%5Cfrac%7B2%7D%7B5%7D%20%2B1%20%5D)
![mgh_s = \frac{1}{2} mv^2 [\frac{7}{5} ]](https://tex.z-dn.net/?f=mgh_s%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2%20%5B%5Cfrac%7B7%7D%7B5%7D%20%5D)
![gh_s =[\frac{7}{10} ] v^2](https://tex.z-dn.net/?f=gh_s%20%3D%5B%5Cfrac%7B7%7D%7B10%7D%20%5D%20v%5E2)

Considering a circular hoop
The moment of inertial is different for circle and it is mathematically represented as

Substituting this into the conservation equation above
![mgh_c = \frac{1}{2} (mr^2)[\frac{v}{r} ] ^2 + \frac{1}{2} mv^2](https://tex.z-dn.net/?f=mgh_c%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28mr%5E2%29%5B%5Cfrac%7Bv%7D%7Br%7D%20%5D%20%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2)
Where
is the height where the circular hoop would be released to equal the speed of the sphere at the bottom



Recall that 


Substituting values

Answer:
Explanation:
electric field at the location of electron
= 9 x 10⁹ x 7.2 / .03²
= 72 x 10¹² N/C
force on electron = electric field x charge on electron
= 72 x 10¹² x 1.6 x 10⁻¹⁹
= 115.2 x 10⁻⁷ N .
C )
work done = charge on electron x potential difference at two points
potential at .03 m
= 9 x 10⁹ x 7.2 / .03
= 2.16 x 10¹² V
potential at .001 m
= 9 x 10⁹ x 7.2 / .001
= 64.8 x 10¹² V
potential difference = (64.8 - 2.16 )x 10¹² V
= 62.64 x 10¹² V .
work done = 62.64 x 10¹² x 1.6 x 10⁻¹⁹
= 100.224 x 10⁻⁷ J .
D )
There will be no change in the magnitude of force on positron except that the direction of force will be reversed . In case of electron , there will be repulsion and in case of positron , there will be attraction .
Work done in case of electron will be positive and work done in case of positron will be negative .
electric field due to charge will be same in both the cases .