Distance covered by a moving object versus friction in an inclined plane

In summary, an object with a mass of 5 kg is pushed up a 30 degree inclined plane with a force of 20.25 N. The initial velocity is 2.0 m/s and the coefficient of kinetic friction is 0.25. To solve for the distance the object will travel up the plane, the following steps need to be taken: find the acceleration along the plane using Newton's second law (F = ma), determine the components of the weight force (mg) perpendicular and parallel to the plane, calculate the magnitude and direction of the frictional force using the given coefficient and normal force, and finally, calculate the net acceleration up the plane using the components of the weight force and the frictional force.
  • #1
ffrancis
11
0

Homework Statement


A 5 kg object is pushed up along a plane inclined 30 degrees from the horizontal by a force of 20.25 N. If the velocity is 2.0 m/s at the foot of the plane and the coefficient of kinetic friction between the plane and the object is 0.25, how far up the plane will the object go?


Homework Equations


f = uN


The Attempt at a Solution


f = uN
f = (0.25)(20.25 N)
f = 5.0625 N

I really don't know how to continue the solution. Do I need to use trigonometry here? I think gravity will cause the moving object to decelerate and stop at some point when it goes up. I just don't know what formulas and equations to use before I can arrive at the solution. Thanks in advance.
 
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  • #2
20.25 N is not the normal reaction. It is the force applied to the object. Mass is given. Find the acceleration along the plane.
What is the component of mg perpendicular to the plane?
What is the component of mg parallel to the plane?
What is the magnitude and the direction of the frictional force?
What is the net acceleration up the plane?
 
  • #3


I would approach this problem by first setting up a free body diagram of the object on the inclined plane. This will help us visualize all the forces acting on the object and their directions. We know that the force of gravity is acting downwards and can be broken into components along and perpendicular to the plane. The force of friction is acting parallel to the plane, in the opposite direction of motion. The applied force is acting parallel to the plane, in the direction of motion.

Next, we can use Newton's second law (F=ma) to find the acceleration of the object along the plane. We know the mass of the object (5 kg) and the net force acting on it (20.25 N - 5.0625 N = 15.1875 N) so we can solve for acceleration (a=F/m = 15.1875 N / 5 kg = 3.0375 m/s^2).

Now, we can use kinematic equations to find the distance traveled by the object. We know the initial velocity (2.0 m/s) and the acceleration (3.0375 m/s^2) so we can use the equation v^2 = u^2 + 2as to find the distance traveled (s = (v^2 - u^2)/2a = (0^2 - 2.0^2)/2(3.0375) = -0.657 m). Note that the negative sign indicates that the object will not reach the top of the inclined plane.

To find the distance traveled up the plane, we can use trigonometry. The angle of the inclined plane (30 degrees) and the distance traveled along the plane (-0.657 m) form a right triangle. We can use the equation tan(theta) = opposite/adjacent to find the distance traveled up the plane (x = tan(30 degrees) * -0.657 m = -0.379 m).

Therefore, the object will travel 0.379 m up the inclined plane before coming to a stop.
 

1. What is the relationship between the distance covered by a moving object and friction in an inclined plane?

The distance covered by a moving object on an inclined plane is directly related to the amount of friction present. The greater the amount of friction, the shorter the distance the object will travel. This is because friction acts as a resistive force, opposing the motion of the object and reducing its speed.

2. How does the angle of the inclined plane affect the distance covered by a moving object?

The angle of the inclined plane has a significant impact on the distance covered by a moving object. As the angle of the inclined plane increases, the distance covered by the object decreases due to an increase in the force of friction. This is because a steeper angle results in a greater component of the object's weight acting against the plane, increasing the force of friction.

3. What is the role of the object's mass in the distance it can cover on an inclined plane?

The mass of the object plays a crucial role in determining the distance it can cover on an inclined plane. Heavier objects have a greater weight, resulting in a greater force of friction acting against the inclined plane. This means that heavier objects will cover a shorter distance compared to lighter objects.

4. Does the type of surface on the inclined plane affect the distance covered by a moving object?

Yes, the type of surface on the inclined plane can affect the distance covered by a moving object. Rough surfaces will have a higher coefficient of friction, resulting in a greater force of friction and a shorter distance covered. In contrast, smoother surfaces will have a lower coefficient of friction, allowing the object to cover a greater distance.

5. How can we reduce the impact of friction on the distance covered by a moving object on an inclined plane?

To reduce the impact of friction on the distance covered by a moving object on an inclined plane, we can use lubricants such as oil or grease to decrease the coefficient of friction. Additionally, we can also decrease the angle of the inclined plane or choose a smoother surface to reduce the force of friction acting on the object.

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