Exercise about work and forces

[Felafel]

Homework Statement

An object, (mass=15 kg) is thrown up a 30° inclined plane, with initial velocity=4.6 m/s
The coefficient of friction is μ=0.34. Find the work done on the object by the normal force, the resultant force, the weight and the friction, from the beginning until it stops (so not when it slides back). Which is the distance run by the object?

The Attempt at a Solution

Could anyone please check it? Because I think the results are correct, but I don't know anything about the force which throws the object and I've solved all without taking it into account.

The work of the normal force is 0 because the angle between it and the direction of the motion is 90°

Then I use the formula ##\Delta K=W_{ris}## with ##K_f = 0## because ##v_f=0##
so ##W_{ris}=\frac{1}{2}\cdot m \cdot v_i^2=159J##

The work of the resultant force is equal to the work of the friction + the work of the weight
And

##F_k (friction)=m \cdot g \cdot cos30° \cdot μ## = 43 N
##F_w=m \cdot g \cdot sin30°=74 N##
##F_{ris}=F_w+F_k=117N##
So
##W_{ris}=F_{ris} \cdot r \cdot cos0° \Rightarrow r=1.4 m##

##W_w= r \cdot \ cos180° \cdot F_w = - 104 J##
##W_k= r \cdot \ cos180° \cdot F_k= -60 J##

thank you :)

 

[BruceW]

yep. Very good, all looks correct to me.

Edit: and yes, you are not supposed to take into account the force with which the object is thrown. The idea is that the initial velocity of 4.6 m/s is its velocity after any initial 'throwing force' has been applied to it. (so the initial velocity contains all the information to do with how hard it was thrown).

 

[Felafel]

:D great! thanks again

 

[BruceW]

no worries :) glad I could help (or at least confirm, haha)

 

[Nickie]

I would like to provide some feedback on your solution. Overall, your approach and calculations seem correct, but there are a few areas that could be improved upon.

Firstly, when solving problems involving forces and work, it is important to clearly define the system and the forces acting on it. In this case, the system is the object being thrown up the inclined plane and the forces acting on it are the normal force, weight, and friction. The force that throws the object is not relevant to the problem and can be ignored.

Secondly, when calculating work done by a force, it is important to consider the displacement of the object in the direction of the force. In your solution, you correctly considered the displacement in the direction of the resultant force, but for the work done by friction and weight, you used the distance of the incline instead of the actual displacement of the object. This could lead to slightly inaccurate results.

Additionally, you mentioned that the work done by the normal force is 0 because the angle between it and the direction of motion is 90°. This is not entirely accurate. While it is true that the work done by the normal force is 0 in this particular case, it is not because of the angle between the force and displacement. It is because the normal force is perpendicular to the direction of motion and therefore does not contribute to the work done.

Finally, when calculating the work done by friction and weight, it is important to use the correct signs. In your solution, you used the cosine of 180° instead of 0°, resulting in a negative sign for both works. This is incorrect because the displacement of the object is in the same direction as the forces, so the cosine should be positive.

Overall, your solution is correct, but it could be improved by clearly defining the system and forces, considering the actual displacement of the object, and using the correct signs in your calculations. Keep up the good work!