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
Showing your own work would be more effective than posting the same question twice in three minutes, if you hope to elicit a helpful response.
To find the answers to these questions, we need to break down the problem and analyze the forces involved.
First, let's calculate the gravitational force acting on the mass while on the incline.
1) Gravitational Force:
The gravitational force can be calculated using the formula:
F_gravity = m * g * sin(theta)
Given:
Mass (m) = 100 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Angle of the incline (theta) = 35 degrees
Substituting the values into the formula:
F_gravity = 100 kg * 9.8 m/s^2 * sin(35 degrees)
Calculate the value of sin(35 degrees) and multiply it by the other values to find F_gravity.
2) Work done by gravitational force:
Work done by a force is given by the formula:
Work = Force * Distance * cos(theta)
Since the mass is moving along the incline, the distance can be calculated using the formula:
Distance = length of the incline * sin(theta)
The length of the incline is not given in the question, so we'll assume it as L.
Substituting the values into the formula:
Work_gravity = F_gravity * L * sin(theta) * cos(theta)
Use the calculated value of F_gravity and substitute it into the equation to find the work done by the gravitational force.
3) Normal force:
The normal force is the perpendicular force exerted by the incline on the mass. On an incline, it can be calculated as:
N = m * g * cos(theta)
Substitute the given values into the formula to find the normal force.
4) Work done by the normal force:
Since the normal force is perpendicular to the displacement of the mass, its work done is zero.
5) Frictional force:
The frictional force while the mass is on an incline can be calculated using the formula:
F_friction = mu * N
Given:
Coefficient of friction (mu) = 0.005 (between the ramp and the mass)
Normal force (N) = calculated in the previous step
Substitute the values into the formula to find the frictional force.
6) Work done by the frictional force:
Work_friction = F_friction * L * cos(theta)
Since the mass slides down the incline, the distance is still L, and we multiply it by cos(theta) because the frictional force acts in the opposite direction to the displacement.
7) Net work:
The net work done is the sum of the work done by each force.
Net Work = Work_gravity + Work_friction
Calculate the net work using the previously calculated values.
8) Net force down the ramp:
The net force down the ramp can be calculated as the component of the gravitational force parallel to the incline minus the frictional force.
Net force = F_gravity_parallel - F_friction
Calculate the net force using the previously calculated values.
9) Work done by the net force:
Work_net = Net force * L * cos(theta)
Since the force and displacement are in the same direction, multiply the net force by L and cos(theta) to calculate the work done by the net force.
By following these steps and using the given values, you should be able to find the answers to the given questions. If you have any further questions, feel free to ask.