A 100kg mass starts from rest at the top of an incline plane that makes an angle of 35 degrees with the horizontal, the coefficient of friction of 0.005 between the ramp and the mass. The mass slides down the ramp and then slides to a stop on a surface with coefficient of friction of .9 between the mass and the surface.
How much work is done by the gravitational force while the mass is on an incline?
B) how much work is done by the normal force while the mass is on an incline
c) how much work is done by the frictional force while the mass is on an incline?
D) what is the net work?
E) what is the net force down the ramp?
F how much work was done by the net force while the mass was stil on the incline
more questions to follow
To determine the work done by different forces, we need to break down the problem into individual components.
Given:
Mass (m) = 100 kg
Angle of incline (θ) = 35 degrees
Coefficient of friction between ramp and mass (μ1) = 0.005
Coefficient of friction between mass and surface (μ2) = 0.9
Let's calculate the values step-by-step:
A) Work done by gravitational force:
The force exerted by gravity can be calculated using the formula: F = m * g * sin(θ)
F = 100 kg * 9.8 m/s^2 * sin(35 degrees)
F = 100 kg * 9.8 m/s^2 * 0.574
F = 561.32 N
Now, let's find the work done: W = F * d * cos(θ)
The distance (d) can be calculated using the formula: d = h / sin(θ)
Since the mass starts from rest at the top, let's assume the height (h) is 1 meter.
d = 1 m / sin(35 degrees)
d = 1 m / 0.574
d = 1.74 m
W = 561.32 N * 1.74 m * cos(35 degrees)
W = 561.32 N * 1.74 m * 0.819
W = 818.4 J (Joules)
B) Work done by normal force:
The normal force (N) is perpendicular to the displacement, so the work done by the normal force is zero.
C) Work done by frictional force:
The frictional force (Ff) can be calculated using the formula: Ff = μ1 * N
The normal force can be found using the formula: N = m * g * cos(θ)
N = 100 kg * 9.8 m/s^2 * cos(35 degrees)
N = 100 kg * 9.8 m/s^2 * 0.819
N = 803.46 N
Ff = 0.005 * 803.46 N
Ff = 4.02 N
Now, let's find the work done: W = Ff * d
Since the displacement (d) on the incline is the same as before, d = 1.74 m
W = 4.02 N * 1.74 m
W = 7 J (Joules)
D) Net work:
Net work is the sum of work done by all forces. So, net work is the sum of work done by gravitational force and work done by frictional force.
Net work = Wgravity + Wfriction
Net work = 818.4 J + 7 J
Net work = 825.4 J (Joules)
E) Net force down the ramp:
The net force down the ramp can be calculated using the formula: Fnet = Fgravity - Ff
Fnet = 561.32 N - 4.02 N
Fnet = 557.3 N
F) Work done by net force while the mass was still on the incline:
Work done by the net force can be calculated using the formula: W = Fnet * d
Since the displacement (d) on the incline is the same as before, d = 1.74 m
W = 557.3 N * 1.74 m
W = 969.1 J (Joules)
Please let me know if you have any more questions!
To find the answers to these questions, we can use the basic formulas related to work and forces. Let's break down each question and find the necessary calculations:
A) To find the work done by the gravitational force while the mass is on an incline, we need to calculate the component of the gravitational force parallel to the incline.
The parallel component of the gravitational force can be calculated using the following formula:
Gravitational force parallel = m * g * sin(α)
Where:
m = mass,
g = acceleration due to gravity (approximated as 9.8 m/s^2),
α = angle of the incline.
So, substituting the given values:
Gravitational force parallel = 100 kg * 9.8 m/s^2 * sin(35°)
Calculate the value of sin(35°) in a calculator, and then perform the multiplication.
B) The normal force does no work because it is perpendicular to the displacement.
Therefore, the work done by the normal force is zero.
C) To find the work done by the frictional force while the mass is on an incline, we need to calculate the component of the frictional force parallel to the incline.
The frictional force can be calculated using the formula:
Frictional force = coefficient of friction * normal force
The normal force can be calculated using the formula:
Normal force = m * g * cos(α)
Where:
m = mass,
g = acceleration due to gravity,
α = angle of the incline.
So, substituting the given values:
Normal force = 100 kg * 9.8 m/s^2 * cos(35°)
Frictional force = 0.005 * (100 kg * 9.8 m/s^2 * cos(35°))
Now, multiply the normal force by the coefficient of friction to find the frictional force.
D) The net work can be calculated by adding the work done by the gravitational force and the work done by the frictional force.
Net work = Work by gravitational force + Work by frictional force
E) The net force down the ramp can be calculated using Newton's second law, which states that the net force is equal to mass multiplied by acceleration.
Net force down the ramp = mass * acceleration
Given that the mass is 100kg and the acceleration down the ramp can be found by using the angle of the incline, we can calculate the net force.
F) To calculate the work done by the net force while the mass is still on the incline, we need to know the displacement. Without knowing the displacement or any other information about the motion, it is not possible to calculate the work done by the net force.
Please provide more information regarding the displacement or any other relevant details to calculate the work done by the net force.
You may proceed with any further questions you have.