A 63.8 N crate is pulled up a 5.22 m inclined plane by a worker at constant velocity. If the plane is inclined at an angle of 59 degree to the horizontal and there exists a constant frictional force of 32.6 N between the crate and the surface, what is the force applied by the worker?
F= F(fr) + mgsinα=
=32.6 +63.8sin59=87.3 N
To find the force applied by the worker, we need to consider the forces acting on the crate along the inclined plane.
1. First, let's resolve the weight of the crate into two components:
- The force acting parallel to the inclined plane (F_parallel): This can be found using the formula F_parallel = mg * sin(θ), where m is the mass of the crate and θ is the angle of inclination.
- The force acting perpendicular to the inclined plane (F_perpendicular): This can be found using the formula F_perpendicular = mg * cos(θ).
2. Next, let's consider the frictional force (F_friction) between the crate and the surface. This force opposes the motion and acts parallel to the inclined plane.
3. Since the crate is pulled up the inclined plane by the worker at a constant velocity, the force applied by the worker (F_applied) must be equal in magnitude and opposite in direction to the net force acting downwards along the inclined plane.
4. The net force acting downward is given by the sum of the force parallel to the inclined plane (F_parallel) and the frictional force (F_friction). So we can write the equation F_net = F_parallel + F_friction.
5. Equating the net force to zero (since the crate is moving at constant velocity), we have F_net = 0. Rearranging the equation, we get F_applied = -F_parallel - F_friction.
Now let's calculate the different forces:
Given:
Weight of the crate (W) = 63.8 N
Angle of inclination (θ) = 59 degrees
Frictional force (F_friction) = 32.6 N
Step 1:
F_parallel = W * sin(θ)
F_perpendicular = W * cos(θ)
Step 2:
F_net = -F_parallel - F_friction
Now we can substitute the given values and solve for F_applied:
F_parallel = (63.8 N) * sin(59 degrees)
F_perpendicular = (63.8 N) * cos(59 degrees)
F_net = -F_parallel - F_friction
Finally, we can substitute the calculated values into the equation for F_net to find the force applied by the worker (F_applied).
To find the force applied by the worker, we first need to calculate the force necessary to overcome the force of friction.
1. Calculate the force of friction:
Frictional force = 32.6 N
2. Decompose the weight of the crate into components parallel and perpendicular to the inclined plane:
Weight of crate = 63.8 N
Vertical component = Weight * sin(angle)
Vertical component = 63.8 N * sin(59 degrees)
3. Calculate the component of the weight parallel to the inclined plane:
Parallel component = Weight * cos(angle)
Parallel component = 63.8 N * cos(59 degrees)
4. Since the crate is pulled up the inclined plane at constant velocity, the force applied by the worker is equal in magnitude but opposite in direction to the force of friction:
Force applied by worker = Force of friction
Force applied by worker = 32.6 N
Therefore, the force applied by the worker is 32.6 N.