Mass 50kg Box Slows to Halt on Friction: 14.5m Distance

In summary: I really appreciate your help!In summary, a box of mass 50 kg is slowing down from 10 m/s on a rough horizontal ground with a coefficient of friction of 0.3. The box is initially being slowed by a string providing a tension of 25N horizontally, but then the string breaks and the box comes to a halt under friction alone after traveling a total distance of 14.5m. By using the equations for acceleration and distance traveled, it can be determined that the box traveled 13m before the string broke, assuming the applied force and friction were in the same direction. However, the wording of the problem may have led to some confusion.
  • #1
Shah 72
MHB
274
0
A box of mass 50 kg is slowing down from 10 m/s on a rough horizontal ground. The coefficient of friction between the box and the ground is 0.3. To start with, the box is being slowed by a string providing a tension of 25N horizontally. Then the string breaks and the box comes to a halt under friction alone after a total distance of 14.5m. Find how far the box traveled before the string broke.
 
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  • #2
show your work on this problem, please
 
  • #3
skeeter said:
show your work on this problem, please
I don't understand how to approach this problem.
m=50kg, it says slowing down from 10m/s, so it's decelerating, u=10m/s
Using F=m×a, 25-(0.3×500)=50a, a=-2.5m/s^2. By taking the total distance traveled under friction, I get v=5.24m/s, so making the assumption that the box comes to halt instantly, I got s= 1.05m when subtracted from total distance I get 13.5 m but the ans is 13m
 
  • #4
To get 13m as the solution, the 25N applied force acts in the same direction as the friction force before the string breaks.

$v_f^2 = 10^2 - 2(3.5) \cdot \Delta x_1 \implies v_f^2 = 100 - 7\Delta x_1$

after the string breaks ...

$0^2 = (100 - 7\Delta x_1) - 2(3) \cdot \Delta x_2$

$\Delta x_2 = 14.5 - \Delta x_1 \implies 100 - 7\Delta x_1 = 6(14.5 - \Delta x_1) \implies \Delta x_1 = 13 \, m$

poorly worded problem. imho.
 
  • #5
skeeter said:
To get 13m as the solution, the 25N applied force acts in the same direction as the friction force before the string breaks.

$v_f^2 = 10^2 - 2(3.5) \cdot \Delta x_1 \implies v_f^2 = 100 - 7\Delta x_1$

after the string breaks ...

$0^2 = (100 - 7\Delta x_1) - 2(3) \cdot \Delta x_2$

$\Delta x_2 = 14.5 - \Delta x_1 \implies 100 - 7\Delta x_1 = 6(14.5 - \Delta x_1) \implies \Delta x_1 = 13 \, m$

poorly worded problem. imho.
Thank you so so much!
 

1. What is the concept of friction and how does it affect the motion of the box?

The concept of friction refers to the resistance force that occurs when two surfaces come into contact with each other. In this case, the friction between the box and the surface it is sliding on causes it to slow down and eventually come to a halt.

2. How is the mass of the box related to its motion and the distance it travels?

The mass of the box affects its motion and the distance it travels because it determines the amount of force needed to accelerate or decelerate the box. In this scenario, the 50kg mass of the box requires a greater amount of force to overcome the friction and bring it to a halt, resulting in a longer distance traveled.

3. Can the distance traveled by the box be changed by altering its mass?

Yes, the distance traveled by the box can be changed by altering its mass. A heavier box would require more force to overcome the friction and come to a halt, resulting in a longer distance traveled. On the other hand, a lighter box would require less force and therefore travel a shorter distance before coming to a halt.

4. Is there a way to reduce the friction between the box and the surface it is sliding on?

Yes, there are ways to reduce the friction between the box and the surface it is sliding on. One way is to use a lubricant such as oil or grease to create a slippery layer between the surfaces. Another way is to use smoother surfaces or materials that have a lower coefficient of friction.

5. How does the distance traveled by the box compare to the initial speed at which it was moving?

The distance traveled by the box is directly proportional to its initial speed. This means that the faster the box is moving, the longer the distance it will travel before coming to a halt due to friction. However, other factors such as mass and surface friction can also affect the distance traveled.

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