An object of mass 10.0 kg is released from the top of an inclined plane which makes an angle of inclination of 30 degrees with the horizontal. The object slides along the inclined plane. The questions refer to the instant when the object has traveled through a distance of 2.00 m measured along the slope. The coefficient of kinetic friction between the mass and the surface is 2.0 use g= 10 m/s2 .
How much work is done by the net force on the mass? and How much work is done by the force of friction?
100j
To find the work done by the net force on the mass and the work done by the force of friction, we need to first calculate the net force and the force of friction acting on the object.
1. Calculating the net force:
The net force acting on the object can be determined by considering the forces acting in the direction of motion. These forces include the force of gravity and the force of friction.
a. Force of gravity:
The force of gravity acting on the object can be calculated using the equation: F_gravity = m * g, where m is the mass of the object and g is the acceleration due to gravity.
In this case, the mass is given as 10.0 kg, and g is given as 10 m/s^2. Therefore, F_gravity = 10.0 kg * 10 m/s^2 = 100 N.
b. Force of friction:
The force of friction can be calculated using the equation: F_friction = μ_k * N, where μ_k is the coefficient of kinetic friction and N is the normal force exerted by the inclined plane.
To find N, we need to determine the component of the weight perpendicular to the inclined plane, which is given by N = m * g * cos(theta), where theta is the angle of inclination.
In this case, theta is given as 30 degrees, and cos(30 degrees) = √3/2. Therefore, N = 10.0 kg * 10 m/s^2 * √3/2 ≈ 86.6025404 N.
Now, we can calculate F_friction = 2.0 * 86.6025404 N ≈ 173.205081 N.
c. Net force:
The net force can be calculated as the difference between the force of gravity and the force of friction, since they act in opposite directions. Therefore, Net Force = F_gravity - F_friction = 100 N - 173.205081 N = -73.205081 N.
2. Calculating the work done:
a. Work done by the net force:
Since the force and displacement are in the same direction, the work done by the net force is given by the equation: Work_net = Net Force * Displacement * cos(theta).
In this case, the displacement is given as 2.00 m, and cos(30 degrees) = √3/2. Therefore, Work_net = -73.205081 N * 2.00 m * √3/2 ≈ -200.000001 J.
b. Work done by the force of friction:
The work done by the force of friction can be calculated using the equation: Work_friction = F_friction * Displacement * cos(180 degrees).
Since the force of friction is acting opposite to the displacement, the angle between them is 180 degrees. Therefore, Work_friction = 173.205081 N * 2.00 m * cos(180 degrees) = -346.410162 J.
So, the work done by the net force on the mass is approximately -200.000001 J (negative sign indicates that work is done against the direction of motion), and the work done by the force of friction is -346.410162 J.