Can Physics Solve These Real-World Problems?

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In summary, a student uses his knowledge of physics to get his car unstuck from a snow drift by attaching a rope to the car and a nearby tree, and applying a force perpendicular to the rope. The force on the car can be calculated by knowing the distance between the car and the tree, and the amount of slack in the rope.
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Nanabit
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1. A student gets his car stuck in a snow drift. Not at a loss, having studied physics, he attaches one end of a stout rope to the vehicle and the other end to the trunk of a nearby tree, allowing for a small amount of slack. The student then exerts a force F on the center of the rope in the direction perpendicular to the car-tree line. If the rope is inextensible and if the magnitude of the applied force is 491 N, what is the force on the car? (Assume equilibrium conditions.)

I'm very very bad at summing up the forces. I know that the sum of all forces in both the x and y directions is zero, and the same with torque, but honestly I don't know where to start because I have no experience in this type of problem. Same with #2.

2. A vertical post with a square cross section is 11.0 m tall. Its bottom end is encased in a base 1.50 m tall, which is precisely square but slightly loose. A force 5.60 N to the right acts on the top of the post. The base maintains the post in equilibrium.
Find the force which the top of the right sidewall of the base exerts on the post. (to the left and to the right.) b. Find the force which the bottom of the left sidewall of the base exerts on the post. (to the left and to the right.)

3. A carpenter's square has the shape of an L (d1 = 16.0 cm, d2 = 4.00 cm, d3 = 4.00 cm, d4 = 11.0 cm). Locate its center of gravity. (Hint: Take (x,y) = (0,0) at the intersection of d1 and d4) (d1 is the length of the long part of the L, d2 is the width of it, d4 is the length of the bottom part of the L, and d3 is the width of it.)

I know what the formula is for this, but I am a bit confused because I don't have any masses. Plus, are the x value and y values in the formulas just the distances in the x and y directions??

4. For safety in climbing, a mountaineer uses a 45.0 m nylon rope that is 10.0 mm in diameter. When supporting the 75.0 kg climber on one end, the rope elongates by 1.80 m. Find Young's modulus for the rope material.

y = FLo/change in L A F= 75 kg(9.8 m/s^2); L = 45.0 m; change in L = 1.8 m; A = pi r^2 = 7.85x10^-5. What am I missing?

Thanks. Sorry I'm so clueless.
 
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  • #2
he attaches one end of a stout rope to the vehicle and the other end to the trunk of a nearby tree, allowing for a small amount of slack. The student then exerts a force F on the center of the rope in the direction perpendicular to the car-tree line. If the rope is inextensible and if the magnitude of the applied force is 491 N, what is the force on the car? (Assume equilibrium conditions.)

The vertical "sag" and the angles formed, when the rope just becomes taut, will depend on the value of the "a small amount of slack".

The tension of the rope when taut will in turn depend on the angle between the rope and the horizontal
 
  • #3
1. A student gets his car stuck in a snow drift. Not at a loss, having studied physics, he attaches one end of a stout rope to the vehicle and the other end to the trunk of a nearby tree, allowing for a small amount of slack. The student then exerts a force F on the center of the rope in the direction perpendicular to the car-tree line. If the rope is inextensible and if the magnitude of the applied force is 491 N, what is the force on the car? (Assume equilibrium conditions.)
You can't get a final numerical answer without know both the distance from the car and the "amount of slack" or, at least, the ratio between them.
Draw a picture showing the rope from the car to the tree, then after being pushed a small amount perpendicular to the line. You have two right triangles. You know the force perpendicular to the line is 491 N and you know the "force triangle" is similar to the triangle formed by the rope. The force on the car, divided by 491 N is equal to 1/2 the distance from the car to the tree divided by the "amount of slack".

For example, if distance between the car and the tree is 100 feet and he leaves 0.1 ft slack (1.2 inches), the ratio is 50/0.1= 500. The force on the car is 500*491 N.

Notice that the less slack, the greater the multiplier, yet there must be some non-zero slack for this to work!
 

Related to Can Physics Solve These Real-World Problems?

What is the concept of "Summing up some forces"?

The concept of "Summing up some forces" is based on the principle of Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. This means that when multiple forces act on an object, the resulting motion can be determined by adding up all the individual forces.

What forces should be included when summing up forces?

When summing up forces, all the forces that are acting on the object should be included. This includes both external forces, such as applied forces, and internal forces, such as friction or tension within the object itself.

How do you calculate the net force when summing up forces?

To calculate the net force when summing up forces, you need to add up all the individual forces acting on the object. If the forces are acting in the same direction, you simply add them together. If the forces are acting in opposite directions, you subtract the smaller force from the larger one to find the net force.

What does a positive or negative net force indicate when summing up forces?

A positive net force indicates that the object is experiencing a net acceleration in the direction of the force. This means the object is either speeding up or changing direction. A negative net force indicates that the object is experiencing a net acceleration in the opposite direction of the force, which can result in slowing down or changing direction.

What are some real-life applications of summing up forces?

Summing up forces has many real-life applications, such as calculating the force required to move an object, determining the stability of structures, and predicting the motion of objects in various situations, such as in sports or transportation. It is also used in engineering and physics to understand the behavior of complex systems and design efficient solutions.

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