A block of mass M is sliding down an inclined plane and is
accelerating. Which of the following statements are true?
Choices: True, False.
A. The frictional force must be less than the component of
Mg down the plane
B. The normal force of the plane is greater than the weight
of the block
C. If the block's mass were halved, its acceleration would
not change
D. The surface must be frictionless because the block is
accelerating
E. The acceleration of the block must be less than g
I will be happy to critique your thinking.
A. True
B. False
C. True
D. False
E. True
All your answers are correct. Good job!
Thanks
To determine which statements are true, let's analyze each option one by one:
A. The frictional force must be less than the component of Mg down the plane.
To assess this statement, we need to consider the forces acting on the block. The gravitational force, Mg, can be decomposed into two components: one perpendicular to the plane, which is counteracted by the normal force, and another parallel to the plane. The frictional force opposes the motion down the plane and is equal to the coefficient of friction multiplied by the normal force.
If the block is accelerating, the parallel component of Mg down the plane is greater than the frictional force, so it is true that the frictional force must be less than the component of Mg down the plane. Therefore, statement A is true.
B. The normal force of the plane is greater than the weight of the block.
The normal force is the force exerted by the plane on the block perpendicular to the plane's surface. It is equal in magnitude but opposite in direction to the perpendicular component of Mg.
Since the block is sliding down the inclined plane, the perpendicular component of Mg is less than the weight of the block. Therefore, the normal force is less than the weight of the block, making statement B false.
C. If the block's mass were halved, its acceleration would not change.
To assess this statement, we need to examine the equation for acceleration on an inclined plane:
a = (m*g*sin(theta) - F_friction) / m
Where:
a is the acceleration,
m is the mass of the block,
g is the acceleration due to gravity,
theta is the angle of inclination of the plane,
F_friction is the frictional force.
When the mass m is halved, the numerator of the equation will also be halved. However, the denominator will also be halved, so the mass cancels out. Therefore, the acceleration remains the same. Hence, statement C is true.
D. The surface must be frictionless because the block is accelerating.
This statement is false. If the block is accelerating, it means there is a net force acting in the direction of motion. This force can be provided by a combination of the gravitational force component down the plane and the frictional force. The presence of acceleration does not imply that the surface is frictionless. So, statement D is false.
E. The acceleration of the block must be less than g.
The acceleration of the block depends on the angle of inclination, the mass of the block, and the forces acting on it. It can be calculated using the equation mentioned in statement C. The value of g represents the acceleration due to gravity, and the actual acceleration of the block can be either greater than or less than g, depending on the specific conditions. Therefore, statement E is false.
In summary:
A. True
B. False
C. True
D. False
E. False