What is the final speed of the box at 10m?

In summary, the conversation is discussing how to find the final speed of a 2.0kg mass that has been lifted 10m by a rope with a force that increases from 20 N to 30 N. It is suggested to use the equation F=ma and kinematics equations, and later to consider the work being equal to the integral over distance of force. The concept of an integral is briefly explained. The final answer is 7.3m/s.
  • #1
avsj
26
0

Homework Statement



A force is exerted by a rope lifting a 2.0kg mass a vertical distance of 10m from the ground. A graphs shows F (N) vs d (m). THe F starts at 20 N and goes to 30 N in a straight line as d goes from 0 to 10m. What is the final speed of the box at 10m?

Homework Equations



F=ma
kinematics equations

The Attempt at a Solution



I am thoroughly lost as to how to deal with this one. The force applied is not constant, so the acceleration will also not be constant. I'm guessing there is another way of looking at it... would really appreciate a hint in which direction to start... thanks.. the answer is 7.3m/s by the way
 
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  • #2
Work is equal to the integral over distance of force. Use conservation of energy to compare this with mgh and then use KE=mv^2/2.
 
  • #3
what do you mean work is equal to the integral over distance of force, what is the integral?
 
  • #4
avsj said:
what do you mean work is equal to the integral over distance of force, what is the integral?

No calculus in this course? Then if you graph force versus distance, work is the area under the curve. That's what an integral is.
 

1. How does changing the force affect the lifting of a mass?

Changing the force applied to a mass can either increase or decrease the lifting of the mass. If the force is increased, the mass will be lifted with greater acceleration and possibly to a greater height. If the force is decreased, the lifting of the mass will be slower and may not reach the same height as before.

2. What factors influence the lifting force needed to lift a certain mass?

The lifting force needed to lift a mass is influenced by several factors, including the weight of the mass, the acceleration due to gravity, and any external forces acting on the mass (such as friction or air resistance). Additionally, the shape and size of the mass can also affect the lifting force needed.

3. How does the direction of the force affect the lifting of a mass?

The direction of the force applied to a mass can impact the lifting in several ways. If the force is applied in the same direction as the motion of the mass, it can increase the lifting. If the force is applied in the opposite direction, it can decrease the lifting or even cause the mass to fall. If the force is applied at an angle, it can alter the direction of the lifting and potentially cause the mass to move in a curved path.

4. What is the relationship between force and mass in lifting?

The relationship between force and mass in lifting is described by Newton's Second Law of Motion, which states that force is equal to mass multiplied by acceleration (F=ma). This means that the heavier the mass, the more force is needed to lift it, and the lighter the mass, the less force is needed.

5. Can changing the force cause a mass to be lifted without any external force?

No, according to Newton's First Law of Motion, an object will remain at rest or continue in a state of constant motion unless acted upon by an external force. This means that a mass cannot be lifted without an external force acting upon it, regardless of how much the force is changed.

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