Answer:
a)
b)
c)
d)
e)
Explanation:
Given that:
- initial speed of turntable,
- full speed of rotation,
- time taken to reach full speed from rest,
- final speed after the change,
- no. of revolutions made to reach the new final speed,
(a)
∵ 1 rev = 2π radians
∴ angular speed ω:
where N = angular speed in rpm.
putting the respective values from case 1 we've
(c)
using the equation of motion:
here α is the angular acceleration
(b)
using the equation of motion:
(d)
using equation of motion:
(e)
using the equation of motion:
A compound optical microscope or just a optical microscope is a microscope that uses light and has more than one lens.
Answer:
v_max = (1/6)e^-1 a
Explanation:
You have the following equation for the instantaneous speed of a particle:
(1)
To find the expression for the maximum speed in terms of the acceleration "a", you first derivative v(t) respect to time t:
![\frac{dv(t)}{dt}=\frac{d}{dt}[ate^{-6t}]=a[(1)e^{-6t}+t(e^{-6t}(-6))]](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%28t%29%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Bate%5E%7B-6t%7D%5D%3Da%5B%281%29e%5E%7B-6t%7D%2Bt%28e%5E%7B-6t%7D%28-6%29%29%5D)
(2)
where you have use the derivative of a product.
Next, you equal the expression (2) to zero in order to calculate t:
![a[(1)e^{-6t}-6te^{-6t}]=0\\\\1-6t=0\\\\t=\frac{1}{6}](https://tex.z-dn.net/?f=a%5B%281%29e%5E%7B-6t%7D-6te%5E%7B-6t%7D%5D%3D0%5C%5C%5C%5C1-6t%3D0%5C%5C%5C%5Ct%3D%5Cfrac%7B1%7D%7B6%7D)
For t = 1/6 you obtain the maximum speed.
Then, you replace that value of t in the expression (1):
hence, the maximum speed is v_max = ((1/6)e^-1)a
Answer:
Energy is defined as the ability to do work. Forms of energy could be kinetic energy or potential energy. Thermal or heat energy can originate from a hot object such as the sun. Energy is used to produce work. Electrical energy for lighting purposes and heating in homes and factories.
Explanation:
Energy is defined as the ability to do work and can be in various forms such as kinetic energy, potential energy, thermal, chemical, electrical energy etc.
Energy origination depends on the type of energy form in discussion. Thermal or heat energy can originate from a hot object such as the sun or an iron box, chemical energy originates from the interaction of atoms and molecules and electrical energy can be initiated by movements of electrons.
Energy is used to produce work. Different forms of energy can do different tasks such as;
Heat energy for heating water
Electrical energy for lighting purposes
Geothermal energy for producing heat and electricity
Nuclear energy for production of nuclear power
Chemical energy for facilitating chemical reactions
Answer:
Power = 130 watt
Explanation:
Power is described as the ability to do work, it is also defined as the amount of work in Joules done in a given time in seconds. Mathematically, it is represented as:
In this example, power is calculated as follows:
Work = 39000 J
Time = 5 minutes
converting the time from minutes to seconds:
1 minute = 60 seconds
∴ 5 minutes = 60 × 5 = 300 seconds
N:B the unit for power can also be represented as Joules/seconds or J/s or JS⁻¹
