A helicopter is lifting two crates simultaneously. One crate with a mass of 151 kg is attached to the helicopter by cable A. The second crate with a mass of 79 kg is hanging below the first crate and attached to the first crate by cable B. As the helicopter accelerates upward at a rate of 2.0 m/s2, what is the tension in each of the two cables?
Cable A .....in kN
Cable B .....in kN
tension= massbelow*a
To solve this problem, we need to calculate the tension in each cable separately. Let's start with Cable A.
To find the tension in Cable A, we need to consider the weight of the first crate and the acceleration of the helicopter. The tension in Cable A will be equal to the sum of the weight of the first crate and the force required to accelerate it upward.
The weight of an object is given by the formula W = m * g, where W is the weight, m is the mass, and g is the acceleration due to gravity. In this case, we need to calculate the weight of the first crate.
Weight of the first crate = (mass of the first crate) * (acceleration due to gravity)
Weight of the first crate = 151 kg * 9.8 m/s^2 (acceleration due to gravity is approximately 9.8 m/s^2)
Weight of the first crate = 1481.8 N
Now, let's calculate the force required to accelerate the first crate upward. The force is given by the formula F = m * a, where F is the force, m is the mass, and a is the acceleration.
Force required to accelerate the first crate upward = (mass of the first crate) * (acceleration)
Force required to accelerate the first crate upward = 151 kg * 2.0 m/s^2
Force required to accelerate the first crate upward = 302 N
The tension in Cable A is equal to the sum of the weight of the first crate and the force required to accelerate it upward.
Tension in Cable A = (weight of the first crate) + (force required to accelerate the first crate upward)
Tension in Cable A = 1481.8 N + 302 N
Tension in Cable A = 1783.8 N
Now let's move on to Cable B.
To find the tension in Cable B, we need to consider the weight of both crates and the acceleration of the helicopter.
The weight of the second crate is calculated in the same way as the first crate:
Weight of the second crate = (mass of the second crate) * (acceleration due to gravity)
Weight of the second crate = 79 kg * 9.8 m/s^2
Weight of the second crate = 774.2 N
The tension in Cable B is equal to the sum of the weight of the second crate and the force required to accelerate it upward.
Tension in Cable B = (weight of the second crate) + (force required to accelerate the second crate upward)
Tension in Cable B = 774.2 N + 79 kg * 2.0 m/s^2
Tension in Cable B = 774.2 N + 158 N
Tension in Cable B = 932.2 N
Finally, let's convert the tensions from Newtons to kilonewtons (kN). Since 1 kilonewton (kN) is equal to 1000 Newtons (N), we divide the tensions by 1000.
Tension in Cable A = 1783.8 N / 1000
Tension in Cable A = 1.7838 kN
Tension in Cable B = 932.2 N / 1000
Tension in Cable B = 0.9322 kN
Therefore, the tension in Cable A is approximately 1.7838 kN, and the tension in Cable B is approximately 0.9322 kN.