Force, acceleration, and friction help1

[catandphysics]

Homework Statement

A space shuttle weighing 7.3 x 10^8 kg takes off from Cape Canaveral. If the air resistance is 1.2 x 10^5 N and the thrust is 8.9 x 10^11 N, how long will it take the shuttle to reach a velocity of 4500 m/s?

Homework Equations

at + vi = vf
ƩFy=mg
ƩFx=ma

The Attempt at a Solution

I know I have to subtract Fg and Ff (or are they the same thing?) from Fa (or N? normal force?) and set that equal to mass x gravity. Is gravity just -9.8m/s/s? And then I have to put that into at + vi = vf (acc. x time + initialvelocity = finalvelocity) but I'm just really lost.

 

[cepheid]

Welcome to PF catandphysics!

Homework Statement

A space shuttle weighing 7.3 x 10^8 kg takes off from Cape Canaveral. If the air resistance is 1.2 x 10^5 N and the thrust is 8.9 x 10^11 N, how long will it take the shuttle to reach a velocity of 4500 m/s?

Homework Equations

at + vi = vf
ƩFy=mg
ƩFx=ma

Careful. This bit in red is not correct (at least, not in general).

The thing that ALWAYS applies is Newton's 2nd law:

F_net = ƩF = ma​

(where I've used boldface to indicate vectors). This is the mathematical way of expressing the statement that "the net force acting on a body (i.e. the vector sum of all forces acting on it) is equal to the body's mass times its acceleration." We can apply this law separately for the horizontal and vertical directions:

ƩF_x = ma_x
ƩF_y = ma_y​

We'll assume here that the shuttle's motion is entirely vertical, so that we can disregard the horizontal direction (i.e. this is essentially a 1D problem). So we just have the one equation for the vertical direction:

ƩF = ma​

where I've dropped the 'y' subscripts since we're only dealing with one direction anyway. I've also dropped the vector notation, because in 1D it is sufficient represent the forces and the acceleration using signed scalars, where the sign tells you the direction (up or down).

So now we need to figure out what all of the vertical forces acting on the shuttle are, so that we can sum them up (and hence solve for the shuttle's acceleration 'a', which is what we are looking for). Draw a free body diagram of the shuttle, with all of the vertical forces acting on it represented. This is the best way to take an inventory of all the forces acting on the body -- it ensures that you don't miss anything.

The Attempt at a Solution

I know I have to subtract Fg and Ff (or are they the same thing?) from Fa (or N? normal force?) and set that equal to mass x gravity. Is gravity just -9.8m/s/s? And then I have to put that into at + vi = vf (acc. x time + initialvelocity = finalvelocity) but I'm just really lost.

You are confused aren't you?

F_f usually refers to the frictional force, which is not relevant here, because the shuttle is not in contact with/sliding against another solid surface. On the other hand, you could think of air resistance (drag) as a "frictional force", so if you want to call it that, then that's fine. F_g is the gravitational force acting on the shuttle (i.e. it is the shuttle's weight). There is no normal force here, because the shuttle is in flight, rather than resting on the ground. The acceleration due to gravity is g = -9.81 m/s².

Again, just apply Newton's 2nd law as I explained above. Take an inventory of all the vertical forces acting on the shuttle (from your FBD) and add them together (taking proper account of each of their signs, which tell you whether they point up or down). Set the result equal to ma. Solve for a.

 

[catandphysics]

Okay, so I do Fa - (Fg + Ff) = ƩF = ma, solve, and just plug that into vf^2 = vi^2 + 2aΔd. okay thanks so much for your help!

 

[cepheid]

Okay, so I do Fa - (Fg + Ff) = ƩF = ma, solve, and just plug that into vf^2 = vi^2 + 2aΔd. okay thanks so much for your help!

If F_a is the thrust, then I agree with that sum of forces. I'm assuming you used a subscript 'a' because it is the "applied" force from the engine.

You were right the first time. Once you know a, you want to plug it into v_f = v_i + at in order to solve for t. The other kinematic equation that you stated above won't help you, because it has no t in it, and t is the thing you are trying to find out.

 

[asteriatic]

I can help clarify some of the concepts and equations involved in this problem. First, Fg and Ff are not the same thing. Fg stands for the force of gravity, which is the weight of an object and is equal to mass x gravity (where gravity is typically represented by the value 9.8 m/s^2). Ff stands for the force of friction, which is the resistance force between two surfaces in contact with each other. In this case, it is the air resistance that is acting against the shuttle's motion.

To solve this problem, we can use the equation ƩFx = ma, where ƩFx represents the sum of all forces acting on the shuttle in the horizontal direction. In this case, we have thrust (Fa) acting in the positive direction and air resistance (Ff) acting in the negative direction. So the equation becomes Fa - Ff = ma. We can substitute the given values for Fa and Ff, and solve for the acceleration (a).

Next, we can use the equation at + vi = vf to find the time it takes for the shuttle to reach a velocity of 4500 m/s. We know the initial velocity (vi) is 0 m/s, and we have just solved for the acceleration (a). We can plug these values into the equation and solve for time (t).

I hope this helps clarify some of the concepts involved in this problem. Remember to always pay attention to the direction and sign of forces when using equations to solve problems. Good luck with your homework!