Two wood blocks of equal mass are pulled up the inclined planes shown with little to no friction involved.
A diagram shows the 2 inclined planes. Plane A is 1 meter high. Plane B is 2 meters high.
Question
How much force is necessary to move Block A up the plane?
Answer options with 4 options
A.
It is equal to the force needed to move Block B.
B.
It is smaller than the force needed to move Block B.
C.
It is two times larger than the force needed to move Block B.
D.
It is three times larger than the force needed to move Block B.
The force needed to move an object up an inclined plane is given by the formula:
Force = mass * acceleration due to gravity * sin(angle of inclination)
Since the two wood blocks have equal mass and are being pulled up inclined planes of different heights, the only difference between the two scenarios is the angle of inclination.
Using trigonometry, we can calculate the angles of inclination for planes A and B:
Angle of inclination for Plane A = arctan(1/1) = 45 degrees
Angle of inclination for Plane B = arctan(2/1) = 63.4 degrees
Now, let's compare the forces needed to move blocks A and B using the formula mentioned above:
Force for Block A = mass * acceleration due to gravity * sin(45)
Force for Block B = mass * acceleration due to gravity * sin(63.4)
Since the sine of 45 degrees is smaller than the sine of 63.4 degrees, the force needed to move Block A (on Plane A) will be smaller than the force needed to move Block B (on Plane B).
Therefore, the answer is B. It is smaller than the force needed to move Block B.