A block of mass 39 kg lies on an inclined plane, as shown. The horizontal and vertical supports for the plane have lengths of 36 m and 15 m, respectively, and the coefficient of kinetic friction between the plane and the block is 0.3. The magnitude of the force ~F necessary to pull the block up the plane with constant speed is most nearly
To find the magnitude of the force necessary to pull the block up the plane with constant speed, we can break it down into two main components: the force of gravity and the force of friction.
First, let's find the force of gravity acting on the block. The force of gravity can be calculated using the equation:
Force of gravity = mass * acceleration due to gravity
Given that the mass of the block is 39 kg and acceleration due to gravity is approximately 9.8 m/s^2, we can calculate:
Force of gravity = 39 kg * 9.8 m/s^2 = 382.2 N
Next, let's find the force of friction. The force of friction can be calculated using the equation:
Force of friction = coefficient of friction * normal force
The normal force can be determined by resolving the weight of the block into its components perpendicular and parallel to the inclined plane.
Perpendicular component = force of gravity * cos(angle of inclination)
Parallel component = force of gravity * sin(angle of inclination)
The angle of inclination can be determined using the trigonometric relationship:
angle of inclination = arctan(vertical support/horizontal support)
In this case, vertical support = 15 m and horizontal support = 36 m. Plugging these values into the equation, we have:
angle of inclination = arctan(15 m/36 m) ≈ 22.6 degrees
Now, let's calculate the normal force:
normal force = Perpendicular component = force of gravity * cos(angle of inclination)
normal force = 382.2 N * cos(22.6 degrees) ≈ 349.2 N
Finally, we can calculate the force of friction:
Force of friction = coefficient of friction * normal force
Given that the coefficient of kinetic friction is 0.3, we have:
Force of friction = 0.3 * 349.2 N ≈ 104.8 N
To maintain a constant speed, the force necessary to overcome friction should be equal to the force of friction. Therefore, the magnitude of the force necessary to pull the block up the plane with constant speed is approximately 104.8 N.
Is this multiple choice? What are the choices?
The force required to pull it up the plane at constant speed is the sum of the friction force
m g cosA*mu
and the component of the weight force down the plane
m g sin A
Get the value of the angle A from your fgure