Answer:
A: The frequency of the vibration is 1.3329 Hz
B: The total energy of the vibration is 18.39375 J
Explanation:
The force of the man his weight causes the raft to sink, and that causes the water to put a larger upward force on the raft. This extra force is a restoring force, because it is in the opposite direction of the force put on the raft by the man. Then when the man steps off, the restoring force pushes upward on the raft, and thus the raft – water system acts like a spring, with a spring constant found as follows:
k= F/x = ((75 kg) * (9.81 m/s²))/(5*10^-2 m) = 14715 N/m
The frequency of the vibration is determined by the spring constant (k) and the mass of the raft (210kg).
fn = 1/2π * √(k/m) = 1/2π * √(14715 / 210) = <u>1.3329 Hz</u>
<u>The frequency of the vibration is 1.3329 Hz</u>
<u />
<u>b) </u>
Since the gravitational potential energy can be ignored, the total energy will be :
Etot = 1/2 k* A² = 1/2 * (14715 )*(0.05)² = 18.39375 J
<u>The total energy of the vibration is 18.39375 J</u>
Answer:
-22.2 m/s²
Explanation:
The equation for position x for a constant acceleration a, time t and initial velocity v₀, initial position x₀:
(1) 
For rocket A the initial and final position: x = x₀= 0. Using these values in equation 1 gives:
(2) 
Solving for time t:
(3) 
The times for both rockets must be equal, since they start and end at the same location. Using equation 3 for rocket A and B gives:
(4) 
Solving equation 4 for acceleration of rocket B:
(5) 
The outer rigid layer of the earth is divided into a couple of dozen “plates” that move around across earths surface relative to each other.
Velocity ratio is also defined as the ratio of a distance through which any part of a machine moves, to that which the driving part moves during the same time. An object has a mechanical advantage if it exerts a force higher than the velocity ratio.
