A fuse is an electrical safety device which should not blow, which should overheat and melts if current is too high. Its placed in the live wire before the switch. This prevents overheating and catching fire. A fuse have a specific current value for example - 3000 amps. So when choosing a suitable fuse you must use the above minimum value but less than maximum value. For example in a circuit there is 1000W flowing, you should choose more than 1000 amps fuse not less or else, it will melt.
it is just a matter of integration and using initial conditions since in general dv/dt = a it implies v = integral a dt
v(t)_x = integral a_{x}(t) dt = alpha t^3/3 + c the integration constant c can be found out since we know v(t)_x at t =0 is v_{0x} so substitute this in the equation to get v(t)_x = alpha t^3 / 3 + v_{0x}
similarly v(t)_y = integral a_{y}(t) dt = integral beta - gamma t dt = beta t - gamma t^2 / 2 + c this constant c use at t = 0 v(t)_y = v_{0y} v(t)_y = beta t - gamma t^2 / 2 + v_{0y}
so the velocity vector as a function of time vec{v}(t) in terms of components as[ alpha t^3 / 3 + v_{0x} , beta t - gamma t^2 / 2 + v_{0y} ]
similarly you should integrate to find position vector since dr/dt = v r = integral of v dt
r(t)_x = alpha t^4 / 12 + + v_{0x}t + c let us assume the initial position vector is at origin so x and y initial position vector is zero and hence c = 0 in both cases
r(t)_y = beta t^2/2 - gamma t^3/6 + v_{0y} t + c here c = 0 since it is at 0 when t = 0 we assume
r(t)_vec = [ r(t)_x , r(t)_y ] = [ alpha t^4 / 12 + + v_{0x}t , beta t^2/2 - gamma t^3/6 + v_{0y} t ]
Answer:
Density is defined as:
Density = Mass/Volume
Now, density is an intensive property, this means that if you have 10 grams of a given material or 1000 grams of the same material, in both cases you will find the same density.
Then a roll of 50 pennies has the same density that a single penny.
The measures of a single penny are:
Mass = 2.5 g
Thickness = 1.52 mm
Radius = 9.525 mm
The coin is a cylinder, and the volume of a cylinder is:
V = pi*r^2*h
where:
pi = 3.14
r = radius = 9.525mm
h = thikness = 1.52mm
The volume is:
V = 3.14*(9.525mm)^2*1.52mm = 433.015 mm^3
The density will be:
D = 2.5g/433.015mm^3 = 0.00577 g/mm^3
Complete Question
The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader–a physicist, naturally–immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.08m. She sets the pendulum swinging, and her collaborators carefully count 101 complete cycles of oscillation during 2.00×102 s. What is the result? acceleration due to gravity:acceleration due to gravity: m/s2
Answer:
The acceleration due to gravity is 
Explanation:
From the question we are told that
The length of the simple pendulum is 
The number of cycles is 
The time take is 
Generally the period of this oscillation is mathematically evaluated as
substituting values
The period of this oscillation is mathematically represented as
making g the subject of the formula we have
![g = \frac{L}{[\frac{T}{2 \pi } ]^2 }](https://tex.z-dn.net/?f=g%20%3D%20%5Cfrac%7BL%7D%7B%5B%5Cfrac%7BT%7D%7B2%20%5Cpi%20%7D%20%5D%5E2%20%7D)
Substituting values
