1. Find the pressure exerted on the ground (in psi) by a 250 lb person who is sitting on a chair whose 4 legs touch the ground with area of '1 by2' each.

2.a)A large 50 kg crate is at rest on level ground. Two people push on the crate. One pushes north with 200 N while the other pushes South with 50 N. If there is no friction, draw a diagram of this object labeling all forces with names and values.

b) Find the acceleration and direction of acceleration for the crate.

1.250 lb=113.4 kg.

mg =113.4•9.8 =1111.32 N.
A =1•2=2 sq.in =0.0013 m²
P=mg/4A =1111.32/4•0.0013 =213715 Pa
2.
The forces acting on the crate are:
F1, F2, gravity (downwards), normal force N (upwards)
Net horizontal force is
F=F1-F2 =200-50 = 150 N (to the North)
a=F/m=150/50 =3 m/s²(to the North).

1. Well, the pressure being exerted on the ground by a 250 lb person sitting on a chair can be calculated! But instead of giving you a boring explanation, let me spin it into a clown joke for you:

Why did the chair go to therapy?

Because it was feeling a lot of pressure from a 250 lb person! Ba-dum-tss!

Now, back to the question. To find the pressure, we'll use the formula: Pressure = Force/Area.

Since each leg of the chair has an area of 1 by 2, the total area of all legs is 4 x (1 by 2) = 4 square units.

So, the pressure exerted on the ground by the person would be the weight (250 lb) divided by the total area (4 sq units). However, since we need the answer in psi, we'll convert pounds to pounds per square inch. 1 psi is equal to about 144 pounds per square inch (it's a strange unit, I know).

So, the final pressure exerted on the ground by the person would be (250 lb / 4 sq units) x (1 psi / 144 lb). Now, let's do the math and find the answer!

2. Ah, a physics problem involving forces! Let's dive right into it.

a) Since we have two people pushing the crate in opposite directions, we'll label the force exerted by the person pushing north as "F North" with a value of 200 N, and the force exerted by the person pushing south as "F South" with a value of 50 N.

Here's a diagram of the crate, with the forces labeled:
```
| |
FNorth| Crate | FSouth
| |
------------
```

b) Since there is no friction, the net force on the crate will be the vector sum of the two forces. We can calculate it using the formula: Net Force = F North - F South

So, the net force on the crate would be 200 N - 50 N = 150 N.

Now, to find the acceleration, we can use Newton's second law: F = ma, where F is the net force, m is the mass of the crate (50 kg), and a is the acceleration.

Plugging in the values, we have: 150 N = 50 kg x a. Solving for a, we get a = 3 m/s^2.

The direction of acceleration would depend on the orientation of the forces. Since the force pushing north (F North) is greater than the force pushing south (F South), the crate would accelerate in the north direction.

And there you have it - the acceleration and direction of acceleration for the crate!

1. To find the pressure exerted on the ground, we need to divide the weight of the person by the total area of the chair's legs that touch the ground.

Weight of the person = 250 lb
Area of each leg = 1 ft * 2 ft = 2 ft² (since 1 ft = 12 inches)
Total area of all 4 legs = 4 * 2 ft² = 8 ft²

To convert the weight to pounds to force in pounds, we can use the conversion factor 1 lb = 4.448 N (approximately).

Weight of the person = 250 lb * 4.448 N/lb = 1112 N

Pressure = Force / Area

Pressure = 1112 N / 8 ft²

To convert the area from square feet to square inches, we can use the conversion factor 1 ft² = 144 in².

Pressure = 1112 N / (8 ft² * 144 in²/ft²)

Pressure = 0.964 N/in²

To convert the pressure from newtons per square inch to pounds per square inch, we can use the conversion factor 1 N/in² = 0.000145038 lb/in² (approximately).

Pressure = 0.964 N/in² * 0.000145038 lb/in²/N

Pressure = 0.000139888 lb/in² (approximately)

Therefore, the pressure exerted on the ground by the person sitting on the chair is approximately 0.000139888 pounds per square inch (psi).

2.a) Here is a diagram of the scenario:

↑ 200 N
┌─┐
┌─┼─┼─┼─┐
│░░░░░│
│░░░C░░│
│░░░░░│
└─┼─┼─┼─┘
└─┘
↓ 50 N

The forces are labeled as follows:
- The person pushing north with 200 N is labeled as "↑ 200 N."
- The person pushing south with 50 N is labeled as "↓ 50 N."
- The weight of the crate is labeled as "C."

b) Since there is no friction and the crate is on level ground, the net force acting on the crate is the difference between the applied forces:

Net force = (200 N) - (50 N) = 150 N (northward)

The acceleration of the crate can be found using Newton's second law:
Force = mass * acceleration

150 N = 50 kg * acceleration

Solving for acceleration:
acceleration = 150 N / 50 kg

acceleration = 3 m/s² (northward)

Therefore, the acceleration of the crate is 3 m/s² in the northward direction.

1. To find the pressure exerted on the ground, we need to divide the force exerted by the person (in pounds) by the total area in square inches that the chair legs cover.

Step 1: Convert the weight of the person from pounds to pounds-force.
Since weight is a force, we need to convert the person's weight (in pounds) to pounds-force by multiplying it by the acceleration due to gravity. The acceleration due to gravity is approximately 32.2 ft/s^2 or 9.8 m/s^2.

Weight in pounds-force = weight in pounds × acceleration due to gravity

In this case, the weight of the person is 250 pounds.

Weight in pounds-force = 250 pounds × 1 pound-force/1 pound (acceleration due to gravity cancels out)

Weight in pounds-force = 250 pounds

Step 2: Calculate the total area in square inches that the chair legs cover.
Given that each leg has an area of 1 by 2 square inches, and there are 4 legs, we can calculate the total area covered by multiplying the area of a single leg by the number of legs.

Total area covered in square inches = area of a single leg in square inches × number of legs

Total area covered in square inches = (1 inch × 2 inches) × 4 legs

Total area covered in square inches = 8 square inches

Step 3: Calculate the pressure exerted on the ground.
Pressure is defined as force divided by area.

Pressure in psi = force in pounds-force / area in square inches

Pressure in psi = 250 pounds / 8 square inches

Pressure in psi = 31.25 psi

Therefore, the pressure exerted on the ground by the 250 lb person sitting on the chair would be approximately 31.25 psi.

2a) When two people push on the crate in opposite directions, the forces on the crate can be represented as follows (assuming the north direction is positive and the south direction is negative):

200 N (North)
---------------------------------
| |
| |
| Crate |
| |
---------------------------------
-50 N (South)

b) Since there is no friction, the total force acting on the crate is the vector sum of the forces applied by the two people:

Net Force = 200 N (North) + (-50 N) (South)

Net Force = 200 N - 50 N

Net Force = 150 N (North)

The mass of the crate is given as 50 kg.

To find the acceleration, we can use Newton's second law:

Net Force = Mass × Acceleration

150 N (North) = 50 kg × Acceleration

Acceleration = 150 N (North) / 50 kg

Acceleration = 3 m/s^2 (North)

Therefore, the acceleration of the crate is 3 m/s^2 in the north direction.