A man pushes on a piano of mass 180 so that it slides at a constant velocity of 12.0 down a ramp that is inclined at 11.0 above the horizontal. No appreciable friction is acting on the piano. Calculate the magnitude and direction of this push
A. if the man pushes parallel to the incline,
We take the upward direction to be positive and downward one to be negative. The sign of the force should be entered correctly.
B. if the man pushes the piano up the plane instead, also at 12.0 parallel to the incline,
Part C
if the man pushes horizontally, but still with a speed of 12.0 .
To calculate the magnitude and direction of the push in different scenarios, we can use Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, when the piano is sliding at a constant velocity down the ramp, the acceleration is zero. Therefore, the net force acting on the piano must also be zero.
Let's analyze each scenario:
A. If the man pushes parallel to the incline:
Since there is no friction, the only force acting on the piano is the force of gravity. To keep the piano moving at a constant velocity with no acceleration, the man's push must be equal in magnitude and opposite in direction to the force of gravity along the incline.
The force of gravity can be calculated as:
Force of gravity = mass x acceleration due to gravity = (180 kg) x (9.8 m/s^2) = 1764 N
So, the magnitude of the man's push is 1764 N, and since it opposes the force of gravity, it is downward, so the direction is negative.
B. If the man pushes the piano up the plane instead, also at 12.0 parallel to the incline:
In this case, the net force still needs to be zero for the piano to maintain a constant velocity. However, now the force of gravity acts downward, opposing the man's push. To cancel out the force of gravity, the man needs to apply a force of the same magnitude but in the opposite direction.
So, the magnitude of the man's push is 1764 N, but this time the direction is upward, represented by a positive sign.
C. If the man pushes horizontally, but still with a speed of 12.0:
In this scenario, the force of gravity acts vertically downward and does not directly affect the motion along the ramp. The only force that could affect the motion horizontally is the force of friction, which is stated to be negligible.
Since the piano is moving at a constant velocity horizontally, the net force in the horizontal direction must be zero. Therefore, the magnitude of the man's push is zero, and there is no specific direction associated with it.