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:
1.53 g
Explanation:
Given,
Initial speed = 30 m/s
Final speed = 0 m/s
Period of stretch, t = 2 s
average deceleration = ?
we know
a = -15 m/s²
Deceleration of the jumper = 15 m/s²
Deceleration in terms of g
Hence, the deceleration of the jumper is equal to 1.53 g
The plane's velocity of 35.11 m/s is actually due in a north-eastward direction. The 12 m/s velocity is the vertical component of the plane's velocity, hence it is pointing northwards. We will use the formula:
Vy = Vsin∅
To determine the angle ∅ at which the plane is flying. This is:
12 = 35.11 * sin∅
∅ = 20.0 degrees
The eastward velocity is:
Vx = Vcos∅
Vx = 35.11 * cos(20)
Vx = 33.0 m/s
The plane's eastward velocity is 33.0 m/s
Answer:
57300 N
Explanation:
The container has a mass of 5300 kg, the weight of the container is:
f = m * a
w = m * g
w = 5300 * 9.81 = 52000 N
However this container was moving with more acceleration, so dynamic loads appear.
w' = m * (g + a)
w' = 5300 * (9.81 + 1) = 57300 N
The rating for the cable was 50000 N
The maximum load was exceeded by:
57300 / 50000 - 1 = 14.6%
