On takeoff, the combined action of the engines and the wings of an airplane exert a force of 8.00 x 103 N on the plane upward at an angle of 65.0˚ above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction.
a) What is the weight of the plane? b) What is the horizontal acceleration of the plane?
a) weight; has to equal force up (less air friction) 8E3*sin65
b) ignoring air friction,
f=ma
8E3*cos65=massplane*a
solve for a
a) Well, I heard this plane has been hitting the gym lately, so it's definitely got some weight to it! But in all seriousness, to find the weight of the plane, we need to find the downward force acting on it. This force is equal in magnitude and opposite in direction to the upward force exerted by the engines and wings, which is 8.00 x 10^3 N. So, the weight of the plane is 8.00 x 10^3 N.
b) As for the horizontal acceleration of the plane, let's put on our detective hats. The plane is rising with constant velocity in the vertical direction, but it's still accelerating horizontally. This means there must be some other force acting horizontally on the plane.
Since there are no other forces mentioned, we can assume this horizontal force is due to the engines pushing the plane forward. And hey, since the vertical velocity is constant, this must mean the upward force from the wings perfectly balances the downward force of gravity.
So, to find the horizontal acceleration, we need to know the mass of the plane and the net horizontal force acting on it. Unfortunately, that information is missing from the question. Looks like this case will remain unsolved, my friend!
a) To find the weight of the plane, we can use the force equation:
F = m * g
where F is the force (weight), m is the mass, and g is the acceleration due to gravity.
Since the plane is rising with constant velocity in the vertical direction, we know that the vertical force is balanced. This means that the weight of the plane is equal to the vertical component of the combined force exerted by the engines and wings.
We can find the vertical component of the force using trigonometry:
F_vertical = F * sin(65.0˚)
F_vertical = (8.00 x 10^3 N) * sin(65.0˚)
Calculate the value of F_vertical:
F_vertical = (8.00 x 10^3 N) * 0.9063
F_vertical = 7250 N
So, the weight of the plane is 7250 N.
b) To find the horizontal acceleration of the plane, we need to consider the horizontal forces acting on the plane.
The horizontal force is responsible for the acceleration, so we can use the equation:
F_horizontal = m * a_horizontal
where F_horizontal is the horizontal force, m is the mass, and a_horizontal is the horizontal acceleration.
The horizontal force is equal to the horizontal component of the combined force exerted by the engines and wings.
We can find the horizontal component of the force using trigonometry:
F_horizontal = F * cos(65.0˚)
F_horizontal = (8.00 x 10^3 N) * cos(65.0˚)
Calculate the value of F_horizontal:
F_horizontal = (8.00 x 10^3 N) * 0.4226
F_horizontal = 3381 N
Now, we can find the horizontal acceleration:
3381 N = m * a_horizontal
To find the acceleration, we need to know the mass of the plane. Unfortunately, the mass is not provided in the given information, so we cannot determine the horizontal acceleration without this information.
To find the weight of the plane, we need to use the information given in the problem. The weight of an object can be calculated using the formula: weight = mass x acceleration due to gravity.
a) Let's start by finding the weight of the plane using the given information. Since the plane is rising with constant velocity in the vertical direction, we can assume that the upward force (the combined action of the engines and the wings) is equal to the weight of the plane.
The upward force is given as 8.00 x 10^3 N, and it is exerted at an angle of 65.0˚ above the horizontal. To determine the vertical component of the upward force, we can multiply the magnitude of the force by the sine of the angle:
Vertical component = Upward force * sin(angle)
Vertical component = 8.00 x 10^3 N * sin(65.0˚)
Once we have the vertical component, we can equate it to the weight of the plane:
Weight = Vertical component of upward force
b) To find the horizontal acceleration of the plane, we need to examine the forces acting in the horizontal direction. The only horizontal force in this case is the thrust force generated by the engines, which causes the plane to accelerate.
The horizontal force can be calculated by multiplying the magnitude of the upward force by the cosine of the angle:
Horizontal force = Upward force * cos(angle)
Horizontal force = 8.00 x 10^3 N * cos(65.0˚)
Once we have the horizontal force, we can use Newton's second law (F = ma) to find the horizontal acceleration of the plane:
Horizontal acceleration = Horizontal force / mass
To find the weight of the plane and the horizontal acceleration, substitute the values into the respective formulas and calculate the results.