When empty, a particular helicopter of mass 3770 kg can accelerate straight upward at a maximum acceleration of 1.29 m/s2. A careless crewman overloads the helicopter so that it is just unable to lift off. What is the mass of the cargo?

Question

When empty, a particular helicopter of mass 3770 kg can accelerate straight upward at a maximum acceleration of 1.29 m/s2. A careless crewman overloads the helicopter so that it is just unable to lift off. What is the mass of the cargo?

Answer 1

Thrust= ma+mg= m(a+g) you are given a, mass, and g. solve for thrust.

Now, if cargo is added, so that a is zero.

Thrust=(masscargo+massplane)g
solve for masscargo

Answer 2

Fthrust - mg = m a

Fhrust = m (9.8+1.29)
do that to get Fthrust then

Fthrust - (m+mc)g = (m+mc)0 = 0
so
m + mc = Fthrust/g

Answer 3

To solve this problem, we need to use the concept of force and acceleration.

We know that the maximum acceleration of the helicopter when empty is 1.29 m/s^2. This means that the upward force produced by the engine is equal to the weight of the helicopter when it is empty.

The weight of the helicopter can be calculated using the formula: weight = mass x acceleration due to gravity.

Let's assume the acceleration due to gravity is approximately 9.8 m/s^2.

Weight of the empty helicopter = mass of the empty helicopter x acceleration due to gravity
Weight of the empty helicopter = 3770 kg x 9.8 m/s^2

Now, the crewman overloads the helicopter with cargo, and the helicopter doesn't lift off. This means that the total weight of the helicopter (empty + cargo) equals the maximum upward force it can produce.

Therefore, we can set up the following equation:

Weight of the empty helicopter + weight of the cargo = Maximum upward force

Let's denote the mass of the cargo as 'M'.

Weight of the empty helicopter = 3770 kg x 9.8 m/s^2
Maximum upward force = mass of the empty helicopter x acceleration

Since the weight of the empty helicopter is equal to the maximum upward force, we can write the equation as:

Weight of the empty helicopter + M x 9.8 m/s^2 = 3770 kg x 1.29 m/s^2

Now, we can solve this equation to find the mass of the cargo (M).

First, calculate the weight of the empty helicopter:
Weight of the empty helicopter = 3770 kg x 9.8 m/s^2

Next, substitute the values into the equation and solve for M:

3770 kg x 9.8 m/s^2 + M x 9.8 m/s^2 = 3770 kg x 1.29 m/s^2

Simplify the equation:

36886 kg m/s^2 + 9.8 M m/s^2 = 4876.3 kg m/s^2

Now, isolate the variable M:

9.8 M m/s^2 = 4876.3 kg m/s^2 - 36886 kg m/s^2

9.8 M m/s^2 = -32009.7 kg m/s^2

M = (-32009.7 kg m/s^2) / 9.8 m/s^2

Finally, calculate the value of M:

M ≈ -3266 kg

Since the mass of the cargo cannot be negative, we can conclude that the mass of the cargo is approximately 3266 kg.