Starting from rest, a 5.0 kg block slides 2.5 m down a rough 30.0 degrees incline in 2.0s. Determine (a) the work done by the force of gravity. (b) the mechanical energy lost due to friction, and (c) the work done by the normal force between block and incline.
I know how to do a but I don't know how to do (b) or (c).
(a)(5kg)(9.8m/s^2)(sin30(2.5m)=61.25J
a is Fnet = F
Ah, you're in luck! I happen to know a thing or two about physics. Let's tackle (b) and (c).
(b) To find the mechanical energy lost due to friction, we need to determine the work done by friction. Since work is equal to force multiplied by distance, we can use the equation:
Work = force of friction x distance
Now, the force of friction can be found using the equation:
Force of friction = coefficient of friction x normal force
However, we don't have the coefficient of friction, so let's use a little trick. Since the block slides down the incline, the work done by friction will be equal to the negative of the work done by gravity (because they act in opposite directions).
Work done by friction = -Work done by gravity
= -61.25 J
So, the mechanical energy lost due to friction is -61.25 J. In other words, friction is not being very helpful here.
(c) Now, let's move on to the work done by the normal force. The normal force and the displacement (distance) of the block are perpendicular to each other, which means the work done by the normal force is zero. It turns out the normal force isn't doing any work at all in this case. It's just hanging out, flexing its non-work muscles.
So, the work done by the normal force is a big fat zero. Poor normal force, always being left out of the fun.
I hope that helps! Let me know if you have any more questions.
To determine the mechanical energy lost due to friction, you need to first find the work done by the force of friction. The work done by friction can be calculated using the equation:
Work done by friction = Force of friction x Distance
The force of friction can be found using the equation:
Force of friction = coefficient of friction x Normal force
Given that the block slides down a rough incline, there is a force of friction acting against the motion of the block. The coefficient of friction depends on the surfaces in contact, and in this case, it is not given. So, let's assume a coefficient of friction, denoted as μ.
Since the block is on an incline, the normal force (N) is equal to the component of gravitational force perpendicular to the incline, which can be calculated as:
Normal force = mass x gravitational acceleration x cosine(θ)
where θ is the angle of the incline. In this case, θ = 30 degrees.
Once you have the force of friction, you can calculate the work done by friction by multiplying it with the distance the block traveled.
To determine the work done by the normal force, you can use the same equation:
Work done by the normal force = Normal force x Distance
The distance in this case is also given as 2.5 m.
Now, let's calculate (b) the mechanical energy lost due to friction and (c) the work done by the normal force:
(b) Mechanical energy lost due to friction:
- Calculate the normal force:
Normal force = (mass x gravitational acceleration x cosine(θ)) = (5.0 kg x 9.8 m/s^2 x cos(30 degrees))
Normal force ≈ 42.43 N
- Calculate the force of friction:
Force of friction = (μ x Normal force)
- Calculate the work done by friction:
Work done by friction = (Force of friction x Distance)
(c) Work done by the normal force:
- Calculate the work done by the normal force:
Work done by the normal force = (Normal force x Distance)
To determine the mechanical energy lost due to friction (b) and the work done by the normal force (c), we need to first calculate the gravitational potential energy at the initial and final positions of the block.
The gravitational potential energy is given by the formula:
PE = mgh
Where:
m = mass of the object (5.0 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = vertical distance traveled
(a) The work done by the force of gravity can be calculated as the change in gravitational potential energy:
ΔPE = mgh_final - mgh_initial
In this case, the vertical distance traveled is h = 2.5 m, but since the incline is at an angle of 30 degrees, we need to find the vertical distance traveled along the incline, which is h = 2.5 m * sin(30 degrees). Therefore:
ΔPE = (5 kg) * (9.8 m/s^2) * (2.5 m * sin(30 degrees)) = 61.25 J
You have already correctly calculated this in your question.
Now, let's move on to determining the mechanical energy lost due to friction.
(b) The mechanical energy lost due to friction can be found using the work-energy principle. According to this principle, the work done by friction is equal to the change in mechanical energy.
ΔE = W_friction
The initial mechanical energy is the gravitational potential energy at the starting position, which is:
E_initial = mgh_initial
The final mechanical energy is the sum of the kinetic energy and the gravitational potential energy at the final position, which is:
E_final = (1/2)mv^2 + mgh_final
where:
m = mass of the object (5.0 kg)
v = final velocity attained (which can be calculated using the equation of motion: v = u + at, where u = initial velocity = 0, and a = acceleration along the incline)
The change in mechanical energy is:
ΔE = E_final - E_initial
Since the mechanical energy lost due to friction is opposite to the change in mechanical energy (negative), we have:
ME_lost_due_to_friction = - ΔE = - (E_final - E_initial)
To determine the work done by the normal force (c), we need to know the angle between the normal force and the displacement of the block along the incline surface. Can you provide that information?
W = Fnet * d * cos30.0
Fnet = Fgx - Fk
Fgx= mgsin30.0
Fk= Muk*Fn
Fn= mgcos30.0
OR
Fnet= Fgx ( If the first one is incorrect).