in a daring rescue by helicopter, two men with a combined mass of 172 kg are lifted to safety. a)If the helicopter lifts the menstraight up with constant acceleration, is the tension in the rescue cablegreater than, less than, or equalto the combined weight of the men? Explain. b) Determinethe tension in the cabke if the men are lifted with a constant accelleration of 1.10 m/s squared.
Yes, the tension is greater than the weight because the acceleration is positive.
Fy = ma
Fy = T - mg
ma = T - mg
(172)(1.1) = T - 1687.32
T = 1876.52 N
a) Well, let me tell you, the tension in the rescue cable will definitely be greater than the combined weight of the men. You see, those men aren't exactly lightweight, and helicopters need to work extra hard to lift heavy loads. So, the tension in the cable has to exceed the weight of the men in order to lift them safely. Helicopters are like the ultimate gym bros, always pumping that tension.
b) Now, to determine the tension in the cable, we need to get a little mathematical. The tension can be found using the formula T = m(a + g), where T is the tension, m is the mass, a is the acceleration, and g is the acceleration due to gravity. In this case, the mass of the two men is 172 kg and the acceleration is given as 1.10 m/s^2.
So, plugging in the numbers, we get T = (172 kg)(1.10 m/s^2 + 9.8 m/s^2). By doing some quick calculations, we find the tension in the cable to be approximately equal to 2001.6 N. That's one mighty cable holding up those dudes!
Remember though, always trust the math, not the clown. Stay safe up there!
a) To determine whether the tension in the rescue cable is greater than, less than, or equal to the combined weight of the men, we need to consider the forces acting on the men and apply Newton's second law of motion. According to Newton's second law, the net force acting on an object is equal to its mass multiplied by its acceleration.
In this case, the men are being lifted straight up, so the only forces acting on them are their weight and the tension in the rescue cable. If we assume the tension in the cable is T and the combined mass of the men is 172 kg, then the weight of the men can be calculated using the formula W = mg, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
The weight of the men is given by W = (172 kg) * (9.8 m/s^2) = 1686.4 N.
Since the helicopter is lifting the men with constant acceleration, the net force acting on them is equal to their mass multiplied by their acceleration. So we can write the equation as:
T - W = ma
where T is the tension in the cable, W is the weight of the men, m is the mass of the men, and a is the constant acceleration.
Substituting the known values, we have:
T - 1686.4 N = (172 kg) * a
We know the constant acceleration, a, is positive because the men are being lifted upward. So, if the tension in the cable, T, is greater than the weight of the men, W, then the net force would be positive and allow the men to be lifted. Therefore, the tension in the cable should be greater than the combined weight of the men.
b) To determine the tension in the cable when the men are lifted with a constant acceleration of 1.10 m/s^2, we can use the equation we derived earlier:
T - 1686.4 N = (172 kg) * (1.10 m/s^2)
Simplifying the equation, we get:
T = (172 kg) * (1.10 m/s^2) + 1686.4 N
T = 189.2 N + 1686.4 N
T = 1875.6 N
Therefore, the tension in the cable when the men are lifted with a constant acceleration of 1.10 m/s^2 is 1875.6 N.
This question has been asked and answered already once today.
The cable tension is T = M (g + a)
a = 1.1 m/s^2
M is the mass
g = 9.8 m/s^2
M g is the weight
You do the numbers.