Applying Newtons Laws to solve this

In summary, the frictional force due to the belt on a box weighing 69 N is 3.00 N when the box is on the inclined portion of the belt.
  • #1
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Luggage is transported from one location to another in an airport by a conveyor belt. At a certain location, the belt moves down an incline that makes an angle of 2.5 degrees with the horizontal. Assume that with such a slight angle there is no slipping of the luggage. Determine the magnitude and direction of the frictional force by the belt on a box weighing 69 N when the box is on the inclined portion of the belt for the following situations:
(a) The belt is stationary.
(b) The belt has a speed of 0.65 m/s that is constant.
(c) The belt has a speed of 0.65 m/s that is increasing at a rate of 0.20 m/s^2.
(d) The belt has a speed of 0.65 m/s that is decreasing at a rate of 0.20 m/s^2.
(e) The belt has a speed of 0.65 m/s that is increasing at a rate of 0.57 m/s^2.

So, I was able to figure out the answer to a, and b is 3.00 N, just by doing 69 sin 2.5. So... what would I do for the other 3? c and d are similar, so if I can find one, I better be able to find the other. Still need to find d as well. Ideas? Thanks!
 
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  • #2
Since the box is not moving with respect to the belt, this is a case of static friction.

The direction of the friction force opposes the inertial force of the mass of the box. In 'c', the box is acceleration, and in 'd' it is decelerating, in addition to going down an incline.

The solution to 'e' is similar do that of 'c'.
 
  • #3
I know, but I need to solve this problem. What do I do?
 
  • #4
The frictional force due to gravity is always the same and acting up the plane of the slope. When the belt is moving at constant velocity it is not causing a force to act on the box so you are correct for a) and b). Now if the belt is being accelerated or deccelerated another frictional force is causing the box to stay in the same position relative to the belt. Think about what direction the friction must be acting to cause the box to stay in the same place in relation to the belt. If you then look at all of the forces and work out the mass you should see that you have the correct acceleration.
 

Related to Applying Newtons Laws to solve this

1. How do Newton's Laws apply to real-life situations?

Newton's Laws of Motion can be used to explain and predict the behavior of objects in everyday situations. The first law states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The third law states that for every action, there is an equal and opposite reaction. By understanding these laws, we can analyze and solve problems involving forces, motion, and interactions between objects.

2. How do I know which Newton's Law to use in a given situation?

The key to applying Newton's Laws is to first identify all the forces acting on the object and their directions. Then, determine the net force by adding or subtracting the individual forces. If the net force is zero, then the object will remain at rest or continue moving at a constant velocity according to the first law. If the net force is non-zero, then use the second law to calculate the acceleration of the object. Finally, consider the third law to determine the reaction force to the applied force.

3. What is the difference between mass and weight in Newton's Laws?

Mass is a measure of an object's inertia, or resistance to change in motion. It remains constant regardless of the object's location or the presence of external forces. Weight, on the other hand, is a measure of the force exerted on an object due to gravity. It can vary depending on the object's location and the strength of the gravitational field. In Newton's Laws, mass is used to calculate the acceleration of an object, while weight is used to calculate the force of gravity acting on an object.

4. Can Newton's Laws be applied to non-inertial reference frames?

Yes, Newton's Laws can be applied to non-inertial reference frames, but some additional forces may need to be considered. In non-inertial frames, objects appear to experience fictitious forces, such as centrifugal and Coriolis forces. These forces do not actually exist, but are due to the frame of reference accelerating. In order to accurately apply Newton's Laws, these fictitious forces must be taken into account.

5. How can I use Newton's Laws to solve practical problems?

To solve problems using Newton's Laws, it is important to draw a free body diagram to identify all the forces acting on the object. Then, use the appropriate Newton's Law to calculate the net force and acceleration of the object. From there, you can use equations of motion, such as those for constant acceleration, to solve for unknown variables. It is also helpful to use common sense and real-life experience to check your answers and make sure they are reasonable.

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