What is the theoretical minimum force

In summary, we have discussed the use of the Work- Energy Theorem to find the magnitude of a constant force acting on a student with a mass of 82.500 kg, starting from rest and traveling 37.5m to reach a speed of 97.5m/s. We have also looked at using the same theorem to determine the minimum force needed to lift a 17000 N car with a jack handle and to calculate the speed of a frictionless roller coaster at the top of a hill.
  • #1
ownedbyphysics
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a 82.500 kg student, starts from rest. A constant force acts on him for 37.5m to give him a speed of 97.5 m/s. Use the Work- energy theorem to find the magnitude of the force.

this is my equation which I'm unsure about
1. f*s= .5mv^2f - .5mv^2i
2. f= .5(82.5)(97.5^2)/37.5
I just want to know if I'm right so far, thanks!

What is the theoretical minimum force Matt must provide to the handle of his car jack if he moves his jack handle .45 m each time he lifts his 17000 N car .004m?

I have no idea how to do this one. F=mg?...

Hideaki Fukuda is in a 475.0kg roller coaster that is poised, motionless, atop a 77.50, hill. How fast will the frictionlest coaster be moving at the top of the next hill, 62.250 m high?
I don't understand this problem and I have no idea what equation to use.
help please!
 
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  • #2
ownedbyphysics said:
a 82.500 kg student, starts from rest. A constant force acts on him for 37.5m to give him a speed of 97.5 m/s. Use the Work- energy theorem to find the magnitude of the force.

this is my equation which I'm unsure about
1. f*s= .5mv^2f - .5mv^2i
2. f= .5(82.5)(97.5^2)/37.5
I just want to know if I'm right so far, thanks!

What is the theoretical minimum force Matt must provide to the handle of his car jack if he moves his jack handle .45 m each time he lifts his 17000 N car .004m?

I have no idea how to do this one. F=mg?...

Hideaki Fukuda is in a 475.0kg roller coaster that is poised, motionless, atop a 77.50, hill. How fast will the frictionlest coaster be moving at the top of the next hill, 62.250 m high?
I don't understand this problem and I have no idea what equation to use.
help please!
Your first one looks good. For the jack problem, assuming the mahine is ideal and loses no energy, the work output is equal to the work input. For the last one, it is all about conservation of energy. In the absence of friction, the sum of kinetic energy plus gravitational potential energy is constant.
 
  • #3


To find the theoretical minimum force, we can use the work-energy theorem which states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by the force is equal to the change in kinetic energy of the student. So we can write the equation as follows:

W = ΔK = 0.5mv^2f - 0.5mv^2i

Where:
W is the work done by the force
ΔK is the change in kinetic energy
m is the mass of the student (82.500 kg)
v^2f is the final velocity (97.5 m/s)
v^2i is the initial velocity (0 m/s)

Substituting the values, we get:

W = 0.5(82.500)(97.5^2) - 0.5(82.500)(0^2)
W = 322218.75 J

Since we know that work is equal to force times distance (W = F*d), we can rearrange the equation to solve for the force:

F = W/d

Substituting the values, we get:

F = 322218.75 J / 37.5 m
F = 8591.25 N

So the theoretical minimum force required to give the student a speed of 97.5 m/s over a distance of 37.5 m is 8591.25 N.

For the second problem, we can use the same approach. The work done by the force (the handle of the car jack) is equal to the change in potential energy of the car. So the equation would be:

W = ΔU = mgh

Where:
W is the work done by the force
ΔU is the change in potential energy
m is the mass of the car (17000 N / 9.8 m/s^2 = 1734.69 kg)
g is the acceleration due to gravity (9.8 m/s^2)
h is the height the car is lifted (.004 m)

Substituting the values, we get:

W = 1734.69 kg * 9.8 m/s^2 * .004 m
W = 67.82 J

Again, using W = F*d, we can solve for the force:

F = W/d

Substituting the values, we get:

F
 

1. What is the theoretical minimum force?

The theoretical minimum force is the smallest amount of force required to produce a certain change in an object's motion. It is the minimum amount of force needed to overcome an object's inertia and cause it to move in a specific direction.

2. How is the theoretical minimum force calculated?

The theoretical minimum force is calculated using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration. This means that the minimum force needed to move an object is directly proportional to its mass and the acceleration required.

3. Can the theoretical minimum force be exceeded?

Yes, the theoretical minimum force is just a theoretical concept and it is possible for a force greater than the theoretical minimum to be applied to an object. This may be necessary in real-world situations where other factors, such as friction, come into play and require a greater force to be exerted.

4. What factors affect the theoretical minimum force?

The theoretical minimum force is affected by various factors, including the mass and shape of the object, the type of surface it is on, and the presence of any external forces, such as friction. These factors can impact the amount of force needed to overcome an object's inertia and cause it to move.

5. Can the theoretical minimum force change?

Yes, the theoretical minimum force can change depending on the circumstances. For example, if the mass or shape of the object changes, the theoretical minimum force needed to move it will also change. Additionally, if external factors, such as friction, are altered, the theoretical minimum force may also be affected.

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