Hi I really need this question answer as a check:
a helicopter holding a 70 kilogram package suspended from a rope 5.0 meters long accelerates upward at a rate of 5.2 m/s^2.
a. Determine tension on the rope.
b. When the upward velocity of the helicopter is 30 meters per second, the rope is cut and the helicopter continues to accelerate upwards at a rate of 5.2 m/s^2. Determine the distance between the helicopter and the package 2 seconds after the rope is cut.
a) T - Mg = Ma
a is the upward acceleration, and you know what g is.
Solve for rope tension, T.
b) t = 2.0 seconds after the rope is cut, the helicopter will have risen an addional distance
D1 = V*t + (1/2)at^2
= 30*2 + (1/2)(5.2)*2^2 = 70.4 m
and the package will have risen an additional distance
D2 = 30*2 - (g/2)t^2 = 40.4 m
The difference is the separation.
Thanx! that's what i got, other than the fact that we had a 5 foot difference with the rope already so the total should be 35 m after 2 secs.
bingo
To find the answer, let me explain the process step by step.
a. To determine the tension on the rope, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, the net force is the tension in the rope and the acceleration is the upward acceleration of the helicopter.
The formula for Newton's second law is:
F = m * a
Given:
Mass of the package (m) = 70 kg
Acceleration (a) = 5.2 m/s^2
Plugging in the values, we get:
F = 70 kg * 5.2 m/s^2
Calculating the tension (F) on the rope would be:
F = 364 N (Newton)
Therefore, the tension on the rope is 364 Newtons.
b. To determine the distance between the helicopter and the package 2 seconds after the rope is cut, we can use kinematic equations.
The equation we will use is:
s = ut + (1/2)at^2
Where:
s is the distance,
u is the initial velocity (which is 30 m/s),
a is the acceleration (which is 5.2 m/s^2),
and t is the time (which is 2 seconds).
Plugging in the values, we get:
s = (30 m/s) * (2 s) + (1/2) * (5.2 m/s^2) * (2 s)^2
Simplifying this equation would be:
s = 60 m + 20.8 m
Calculating the distance (s) between the helicopter and the package after 2 seconds, we get:
s = 80.8 meters
Therefore, the distance between the helicopter and the package 2 seconds after the rope is cut is 80.8 meters.