Pulling on a rope attached to a box: Newton's Laws and Incline Planes

In summary, a student pulls a box of books with a force of 130.0 N at an angle of 15.0° above the horizontal, resulting in an acceleration of 2.483572006 m/s/s. When the student moves the box up a 10.0° incline with the same force and angle, the new acceleration is affected by the rope tension, weight, normal force, and frictional force. Drawing a diagram can help in visualizing and solving the problem.
  • #1
wisefallen
1
0

Homework Statement



A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 130.0 N at an angle of 15.0° above the horizontal. The box has a mass of 25.0 kg, and the coefficient of kinetic friction between box and floor is 0.300.
(a) Find the acceleration of the box.

(b) The student now starts moving the box up a 10.0° incline, keeping her 130.0 N force directed at 15.0° above the line of the incline. If the coefficient of friction is unchanged, what is the new acceleration of the box?



Homework Equations



F=ma, Assorted equations derived from Newton's Laws



The Attempt at a Solution



I found the answer to part A to be 2.483572006 m/s/s. In part B, I attempted to determine the forces affecting the situation: rope tension, weight, normal force, and frictional force. I think I get lost trying to find these forces.

Thanks!
 
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  • #2
You will get lost if you don't draw a large diagram. Maybe a couple, as you discard the first when you realize you've marked some things incorrectly. As before, the rope takes some of the "weight", reducing the force the block exerts normal to the incline and thus reducing the force to overcome friction.
 

1. What is the first law of motion in relation to pulling on a rope attached to a box?

The first law of motion, also known as the law of inertia, states that an object will remain at rest or in motion with a constant velocity unless acted upon by an external force. In the case of pulling on a rope attached to a box, the box will remain at rest until a force is applied to it.

2. How does the second law of motion apply to pulling on a rope attached to a box?

The second law of motion, also known as the law of acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. When pulling on a rope attached to a box, the force applied to the box will determine its acceleration. The larger the force, the greater the acceleration.

3. What is the role of friction in pulling on a rope attached to a box?

Friction is the force that opposes the motion of two surfaces in contact with each other. When pulling on a rope attached to a box, friction plays a role in determining the force needed to move the box. The rougher the surface of the box and the ground, the greater the friction and the more force needed to overcome it.

4. How does the angle of the incline plane affect the force needed to pull the box?

The angle of the incline plane, or the angle at which the plane is tilted, affects the force needed to pull the box. As the angle of the incline plane increases, the force needed to pull the box also increases. This is because the component of the force acting parallel to the incline plane, known as the force of gravity, also increases with the angle.

5. How does the third law of motion apply to pulling on a rope attached to a box?

The third law of motion, also known as the law of action and reaction, states that for every action, there is an equal and opposite reaction. In the case of pulling on a rope attached to a box, the force applied to the rope creates an equal and opposite force on the box, causing it to move in the opposite direction.

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