Resultant forces on objects and springs

[slaw155]

Homework Statement

Hi

I've been struggling to work this out over the last week, so any help would be appreciated!

1: An object of mass 400kg is dragged at a constant velocity of 0.5m/s up a rough slope inclined at 25degrees to the horizontal. Given that coefficient of kinetic friction between object and ground = 0.75, at what rate is work done against friction?

Homework Equations

1: Power = work/time

The Attempt at a Solution

I haven't unfortunately gotten past knowing what equation to use :/

 

[HallsofIvy]

Have you drawn a picture with the individual force vectors?

 

[slaw155]

I've tried for question 1 but don't know how to progress with it.

 

[Simon Bridge]

I've tried for question 1 but for question 2 I can't figure out how we can find the extra force exerted on the spring when the mass is pushed down on it (this force is additional to the weight of the object)

You don't need it. Part 2 is not even a force problem - try using energy conservation instead.

 

[HalfLostAndSearching]

Hi there,

Thank you for reaching out for help with this problem. I understand that sometimes certain concepts or problems can be challenging to grasp. Let me try to break down this problem for you and provide some guidance.

Firstly, let's start by defining some key terms and concepts.

Resultant force refers to the net force acting on an object, which is the total of all the individual forces acting on it. In this problem, the resultant force would be the force that is causing the object to move up the slope.

Springs are objects that have the ability to stretch or compress when a force is applied to them. They follow Hooke's law, which states that the force applied to a spring is directly proportional to the displacement of the spring.

Now, let's look at the given information in the problem. We have an object with a mass of 400kg being dragged up a slope at a constant velocity of 0.5m/s. The slope is inclined at an angle of 25 degrees to the horizontal. We are also given the coefficient of kinetic friction between the object and the ground, which is 0.75.

To solve this problem, we need to consider the various forces acting on the object. These include the force of gravity (mg), the normal force (N) from the ground, and the force of friction (Ff) acting in the opposite direction of motion.

Using Newton's second law, we can calculate the resultant force (Fnet) as:

Fnet = ma

Where m is the mass of the object and a is the acceleration. Since the object is moving at a constant velocity, the acceleration is zero. Therefore, the resultant force (Fnet) is also zero.

Now, let's look at the forces acting on the object in more detail. The force of gravity (mg) is always acting downwards, and its magnitude is given by:

mg = 400kg x 9.8m/s² = 3920N

The normal force (N) is the force exerted by the ground on the object, perpendicular to the surface. Since the object is on an inclined plane, the normal force will be less than the force of gravity, and its magnitude can be calculated using trigonometry:

N = mgcosθ = 3920N x cos(25°) = 3537N

Finally, the force of friction (Ff) can be calculated using the formula