A block of mass 2.30 kg is pushed 2.38 m along a frictionless horizontal table by a constant 16.0 N force directed 26.9o below the horizontal. Determine the work done by the applied force.
Determine the magnitude of the normal force exerted by the table.
Determine the magnitude of the force of gravity.
Determine the net force on the block.
To determine the work done by the applied force, we can use the formula:
Work = Force * Distance * cos(theta)
where Force is the magnitude of the applied force, Distance is the distance the object is moved, and theta is the angle between the force direction and displacement direction.
For the given values, the Force = 16.0 N, Distance = 2.38 m, and theta = 26.9o. So we can substitute these values into the formula:
Work = 16.0 N * 2.38 m * cos(26.9o)
Calculating this expression will give us the work done by the applied force.
To determine the magnitude of the normal force exerted by the table, we need to consider that in the absence of friction, the normal force is equal in magnitude and opposite in direction to the gravitational force. The normal force acts perpendicular to the surface of the table, and it counterbalances the weight of the block.
To calculate the magnitude of the normal force, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. Since the block is on a horizontal surface with no vertical acceleration, the normal force cancels out the gravitational force:
Normal force = gravitational force = m * g
where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2). Substituting the given mass value will give us the magnitude of the normal force.
To determine the magnitude of the force of gravity, we can use the formula:
Force of gravity = mass * g
where mass is the mass of the block and g is the acceleration due to gravity. Substituting the given mass value will give us the magnitude of the force of gravity.
To determine the net force on the block, we need to consider all the forces acting on the block. In this case, there are two forces acting on the block: the applied force and the force of gravity (which is equal in magnitude and opposite in direction to the normal force, as explained earlier).
The net force can be calculated by adding these two forces together, taking into account their directionality. If the forces are in the same direction, you can simply add their magnitudes. If the forces are in opposite directions, subtract one from the other. The resulting net force will give you the magnitude and direction of the total force acting on the block.