starting from rest,a 5.20 kg block slides 3.20 m down a rough 30 degrees incline. The coefficient of kinetic friction between the block and the incline is k=0.436.
(a)determine the work done by the normal force
Normal to the plane?
Friction work is parallel to the plane, so any work done by the normal force is zero. However, some movement is down the plane, by gravity, but no work from the normal force.
The angle between gravity and the plane is 60 degrees.
work from gravity= mg*3.2*sin30
http://www.hejackjr.com/Index1/Phy210_Problem_Ch5_5.pdf
To determine the work done by the normal force, we first need to find the normal force acting on the block.
The normal force, represented by FN, is the force exerted by a surface to support the weight of an object resting on it. In this case, the block is resting on the inclined plane.
The weight of the object, represented by mg, can be calculated using the formula:
Weight (mg) = mass (m) x acceleration due to gravity (g)
Given that the mass of the block is 5.20 kg, and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight:
Weight (mg) = 5.20 kg x 9.8 m/s²
Now, we need to determine the component of the weight acting parallel to the incline. This component is responsible for causing the block to slide down the incline.
The component of the weight parallel to the incline, represented by mg*sin(θ), can be found using the formula:
Component of Weight Parallel = Weight (mg) x sin(θ)
Given that the angle of inclination is 30 degrees, we can calculate the component of the weight parallel to the incline:
Component of Weight Parallel = Weight (mg) x sin(30°)
Next, we need to determine the force of kinetic friction acting on the block. The force of kinetic friction, represented by fk, can be calculated using the formula:
Force of Kinetic Friction = coefficient of kinetic friction (k) x normal force (FN)
Given that the coefficient of kinetic friction is k=0.436, we can calculate the force of kinetic friction:
Force of Kinetic Friction = k x normal force (FN)
Now, we can equate the force of kinetic friction to the component of weight parallel to the incline to find the normal force:
k x FN = Component of Weight Parallel
Simplifying the equation and solving for FN:
FN = Component of Weight Parallel / k
Once we have determined the value of the normal force, we can calculate the work done by the normal force.
The work done by the normal force can be calculated using the formula:
Work = Force x Distance
In this case, the force is the normal force and the distance is the displacement of the block down the incline.
Work by the normal force = Normal force x distance
Given that the block slides 3.20 m down the incline, and we have determined the value of the normal force, we can calculate the work done by the normal force.