Rollercoasters generate speed by converting gravitational potential energy into kinetic energy by taking the cart to the top of a large hill and letting it go. The conversion of a perfectly efficient system would be like so:
PE = KE
and using the formulas for potential and kinetic energy:
mgh = 1/2mv^2.
However, the efficiency of this system is 50%, meaning that the kinetic energy obtained from this conversion would appear as so:
PE=0.5 KE
mgh=0.5(1/2mv^2)
mgh=1/4mv^2.
The masses cancel out, leaving:
gh=1/4v^2
The goal is to achieve 65 m/s, and with Earth’s innate gravity of 9.806 m/s^2, we have:
gh=1/4v^2
(9.806)h=1/4(65)^2
h=107.71 meters
The height of the first hill must be 107.7 meters to generate a speed of 65 m/s with a conversion efficiency of 50%.
Hope this helps!
Answer:
The hydro static force on the back of the dam is 
Explanation:
Given that,
Width b= 1000 m
Depth d= 200 m
We need to calculate the average pressure
Using formula of average pressure
Put the value into the formula
We need to calculate the hydro static force on the back of the dam
Using formula of force
Put the value into the formula
Hence, The hydro static force on the back of the dam is
Answer:
1. Potential hazard
2. Mining opportunity
Explanation:
The two reason, why astronomers are so interested in the discovery of additional Earth-approaching asteroids:
1. Potential hazard: We have proof that the dinosaurs got extinct because of an asteroid/comet strike on Earth. Also we have seen the effects of the Tunguska event and Chelyabinsk tragedy. These are enough to show us that asteroids can be very dangerous and wipe out the life from Earth.
2. Mining Opportunity: We have discovered a lot of asteroids which contains a lot of metal and precious elements. There can be a possibility of mining such asteroids in the future and reducing the burden on Earth.
The temperature will increase
Answer:
We know that force applied per unit area is called pressure.
Pressure = Force/ Area
When force is constant than pressure is inversely proportional to area.
1- Calculating the area of three face:
A1 = 20m x 10 m =200 Square meter
A2 = 10 mx 5 m = 50 Square meter
A3 = 20m x 5 m = 100 Square meter
Therefore A1 is maximum and A2 is minimum.
2- Calculate pressure:
P = F/ A1 = 30 / 200 = 0.15 Nm⁻² ( minimum pressure)
P = F / A2 = 30 / 50 = 0.6 Nm⁻² ( maximum pressure)
Hence greater the area less will be the pressure and vice versa.
