Normal forces on aircraft wheels and torque on a spinning CD

[moonlit]

Force & net torque. Please Help!

I have two problems for homework that I just can't seem to figure out. Can someone please help me?! Thanks.

1) A jet transport has a weight of 2.97 x 106 N and is at rest on the runway. The two rear wheels are 17 m behind the front wheel, and the plane's center of gravity is 13.1 m behind the front wheel. Determine the normal force exerted by the ground on (a) the front wheel and on (b) each of the two rear wheels.

2) A CD has a mass of 17 g and a radius of 6 cm. When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 18 rad/s in 0.53 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.

 

[nautica]

There is a homework forum available - you will probably get more help there.

Nautica

 

[M98Ranger]

Sure, I'd be happy to help you with these problems! Let's start with the first one.

1) To find the normal force exerted by the ground on the front wheel, we need to first calculate the total torque acting on the plane. We can do this by using the formula torque = force x distance, where the distance is measured from the pivot point (in this case, the front wheel) to the line of action of the force. Since the plane is at rest, the net torque must be equal to 0.

So, let's set up our equation:

0 = (2.97 x 106 N)(13.1 m) + Ff(17 m)

Where Ff is the unknown normal force exerted by the ground on the front wheel. Solving for Ff, we get:

Ff = -2.05 x 106 N

Since the force is negative, we know it is acting downwards, which makes sense as it is balancing out the weight of the plane.

Now, to find the normal force exerted by the ground on each of the rear wheels, we can use the same equation but this time we will set the distance to be from the pivot point to the line of action of the weight of the plane (since it is acting downwards). So our equation becomes:

0 = Ff(17 m) + (2.97 x 106 N)(13.1 m + 17 m)

Solving for Ff, we get:

Ff = 1.44 x 106 N

So the normal force exerted by the ground on each of the rear wheels is 1.44 x 106 N.

2) To find the net torque acting on the CD, we can use the formula torque = moment of inertia x angular acceleration. The moment of inertia for a uniform solid disk is 1/2MR^2, where M is the mass and R is the radius.

So, our equation becomes:

T = (1/2)(0.017 kg)(0.06 m)^2(18 rad/s^2)

Solving for T, we get:

T = 0.036 J

So the net torque acting on the CD is 0.036 J.

I hope this helps you solve your homework! Remember, it's always important to set up your equations correctly and pay attention to the direction of forces and torques. Good luck!