A block of weight w = 25.0 N sits on a frictionless inclined plane, which makes an angle = 25.0 with respect to the horizontal, as shown in the figure. A force of magnitude F= 10.6 N , applied parallel to the incline, is just sufficient to pull the block up the plane at constant speed.
The block moves up an incline with constant speed. What is the total work done on the block by all forces as the block moves a distance L= 2.60m up the incline? Include only the work done after the block has started moving at constant speed, not the work needed to start the block moving from rest.
What is , the work done on the block by the force of gravity w as the block moves a distance
L= 2.60m up the incline?
To find the total work done on the block by all forces as it moves a distance L up the incline, we need to consider the work done by both the applied force and the force of gravity separately.
1. Work done by the applied force:
The work done by a force can be calculated using the formula W = F * d * cosθ, where F is the magnitude of the force, d is the displacement, and θ is the angle between the force and the displacement.
In this case, the applied force is parallel to the incline, so the angle θ between the force and the displacement is 0° (cos 0° = 1). The displacement is given as L = 2.60 m, and the magnitude of the applied force is F = 10.6 N.
Therefore, the work done by the applied force is:
W_applied = F * L * cosθ = 10.6 N * 2.60 m * 1 = 27.56 J
2. Work done by the force of gravity:
The force of gravity acts vertically downward, while the displacement is along the incline. To calculate the work done by gravity, we need to find the component of the force of gravity parallel to the displacement.
The force of gravity can be resolved into two components: one perpendicular to the incline and one parallel to the incline. The component parallel to the incline (F_parallel) can be calculated as F_parallel = m * g * sinθ, where m is the mass of the block (which can be found using F = w, where w is the weight of the block) and g is the acceleration due to gravity (approximately 9.8 m/s²).
The displacement is L = 2.60 m, and the angle θ between the force of gravity and the displacement is the same as the angle of the incline (25°).
Therefore, the work done by the force of gravity is:
W_gravity = F_parallel * L = (m * g * sinθ) * L
To find the mass of the block, we can use the weight w = 25.0 N:
w = m * g => 25.0 N = m * 9.8 m/s² => m = 25.0 N / 9.8 m/s²
Substituting this value of mass into the expression for the work done by gravity, we get:
W_gravity = [(25.0 N / 9.8 m/s²) * 9.8 m/s² * sin 25°] * 2.60 m
After calculating this expression, you will find the work done by gravity.
Note: The work done by gravity is negative because the direction of gravity is opposite to the direction of displacement.