How to Calculate Velocity of a Rocket Sled After Passing Over a Rough Patch

In summary, a rocket sled weighing 20000N glides at a constant velocity of 24 m/s on ice with negligible friction. When it passes over a rough patch 22m long, a friction force of 6000N acts on it. Using the equation Fnet=ma, the acceleration is calculated to be -2.94 m/s^2. Using the equation Vf^2=Vi^2+2ad, the final velocity of the sled leaving the rough patch is determined to be approximately 22.6 m/s. However, this is slightly higher than the expected answer of 23.7 m/s and may be due to rounding errors.
  • #1
xavior6
9
0

Homework Statement


A Rocket Sled weighing 20000N is gliding at 24 m/s (North) on ice where friction is negligible. Suddenly it passes over a rough patch 22m long, which creates a friction force of 6000N (south). With what velocity does the sled leave the rough patch?


Homework Equations


Vi=Vf+ad
Vf(squared)=Vi(squared)+2ad
Fnet=Ff+Fa
Fnet= Ma


The Attempt at a Solution



I figured that the Vi of the sled when it hits the patch is 24 m/s since there is no acceleration. When it hits the patch, there are two forces on the object; one with -6000N and the other which is the original force applied. The sum of these constitutes the net force. The net force is also equal to the Mass of the object x Acceleration. The mass is 20000/9.81 which equals roughly 2038.7KG.

If I find acceleration, I would easily find the Vf of the object leaving the rough patch. The problem is, I have no idea how to find the forward force of the rocket sled, so I am left with 2 variables in 1 equation and I am stuck.

Can someone please tell me the way to solve this? Thank you.
 
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  • #2
xavior6 said:
I figured that the Vi of the sled when it hits the patch is 24 m/s since there is no acceleration. When it hits the patch, there are two forces on the object; one with -6000N and the other which is the original force applied.
There's only one horizontal force acting on the sled--the friction. There's no "original force" needed to keep the sled moving as it glides over the ice.


The sum of these constitutes the net force. The net force is also equal to the Mass of the object x Acceleration. The mass is 20000/9.81 which equals roughly 2038.7KG.

If I find acceleration, I would easily find the Vf of the object leaving the rough patch. The problem is, I have no idea how to find the forward force of the rocket sled, so I am left with 2 variables in 1 equation and I am stuck.
There is no forward force, just friction. Perhaps you are thinking of the force that was needed to get the sled moving at 24 m/s? Once it got moving, no force is needed to keep going. (Newton's 1st law.)
 
  • #3
Hmm what you say makes complete sense. But i still do not reach the correct answer. Using your advice, the modified solution method would be:

Fnet= -6000N
Fnet= 2038.7Kg(a)
a= -2.94.

Solving this using the Vf(squared)=Vi(squared)+2(a)(d) formula, Vf= 22.6 m/s
The answer is 23.7 m/s, so I am off by a factor of 1.1. Can you point me to the right direction as to what may have caused this deviation? I'm quite sure it can't be rounding errors.
 
  • #4
Your method is perfectly correct. (I'd say that your answer is a bit too high--recheck your arithmetic!) No reason to think that 23.7 m/s is correct. (Also, realistically speaking, only 2 digits--at most--are significant.)
 

1. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity is a measure of how fast an object is moving in a specific direction. In other words, speed is a scalar quantity while velocity is a vector quantity.

2. How do you calculate acceleration?

Acceleration is calculated by dividing the change in velocity by the change in time. This can be represented by the formula a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

3. What is Newton's first law of motion?

Newton's first law of motion, also known as the law of inertia, states that an object at rest will remain at rest, and an object in motion will continue to move at a constant velocity, unless acted upon by an external force.

4. How do forces affect motion?

Forces can cause a change in the motion of an object. A force can cause an object at rest to start moving, or it can change the speed or direction of an object that is already in motion. Forces can also cause an object to stop moving or change its direction of motion.

5. What is the difference between kinetic and potential energy?

Kinetic energy is the energy an object has due to its motion, while potential energy is the energy an object has due to its position or shape. Objects can have both kinetic and potential energy at the same time, and energy can be converted between these two forms.

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