Find the average force the carpet exerts

[Soaring Crane]

1. A 10 kg brick falls from a height of 2 m.

a. Suppose it falls unto a carpet, 1 cm thick. Assuming the force stopping it is constant, find the average force the carpet exerts on the brick. Answer: 2 x 10^4 N

b. Now if it falls onto a 5 cm foam rubber pad, what constant force is needed to bring it to rest? Answer: 4 x 10^3 N

I know the formula F*/\t =/\p. To get F, /\p//\t. But do these objects have any effects on the brick's displacement and the time interval? [In some of these problems, kinematic formulas are needed to find things that are not given besides what one seeks. I used v_f^2 = V_i^2 + 2a/\x to find the velocity (about 63 m/s) if there was no object on the ground.] Please tell me the steps to get the force.

2. A 7600-kg space probe is traveling through space at 120 m/s. Mission control determines that a change in course of 30 degrees is necessary and, by electric communication, instructs the probe to fire rockets perpendicular to its present direction of motion. If the escaping gas leaves the craft's rockets at an average speed of 3200 m/s, what mass of gas should be expelled? Answer: 170 kg

No one, not even the instructor, could figure out how to do this. 60-90-30 triangles, x and y components, and other momentum formulas were used but to no avail. How do you do this?

Thank you for any clues!

 

[upsidedown]

Well, the first one is not quite that easy. You can make some assumptions to build a crude model though.. You can make a guess of intrusion depth (like with the carpet) and assume a constant force (or some other a priori known force function). Every thing else is just setting boundary conditions..

The second one isn't very complicated. If the course change is only due to a perpenticular acceleration, you can simply apply the vector triangle to the velocity vectors. In that case is means, that $$v_y = sin(30°) v_x = .5 \cdot v_x$$. Does that get you where you want to get?

 

[Integral]

In your first problem the work done by gravity accelerating the block must be equal to the work done by the rug stopping it.
$$W_{Rug} = W_{Fall}$$

Remember W=fd

What is the force on the falling object?
What is the distance?

See if you can get to the solution with these hints.

 

[HallsofIvy]

You also have to assume (and it doesn't strike me as completely realistic) that the 1 cm. pad stops the brick IN EXACTLY 1 cm. and the 5 cm. pad stops the brick IN EXACTLY 5 cm. At least those are the only distance measurements given and you have to know the distance in which the object stops.