Optimistic Calculations: Finding Net Force, Acceleration, and Normal Force on a Block

How can we determine the net force, acceleration, and normal force acting on a block being pushed up a frictionless ramp?

Given that Jimmy is pushing a block of 12 kg up a frictionless ramp at an angle of 35° with an applied force of 148 N.

Answer:

The net force acting on the block is 80.9 N, the block's acceleration is 6.74 m/s², and the magnitude of the normal force is 122.3 N.

To find the net force, acceleration, and magnitude of normal force for a block being pushed up a frictionless ramp, we can use various formulas involving the applied force, mass of the block, and angle of the ramp.

Explanation:

To determine the net force, acceleration, and normal force acting on a block moving up a frictionless incline, we must consider the forces in both the direction parallel and perpendicular to the incline. The force exerted by Jimmy and the gravitational force components along the incline need to be taken into account.

First, we calculate the component of the gravitational force acting down the ramp, which is given by mg sin(θ), where m is the mass of the block and g is the acceleration due to gravity. For a mass of 12 kg and θ = 35°, this force is 12 kg × 9.8 m/s² × sin(35°), which equals approximately 67.1 N. Since the ramp is frictionless, the normal force will be equal to the gravitational force component perpendicular to the incline, which is mg cos(θ).

The net force acting on the block is the applied force minus the component of the gravitational force along the ramp, so it will be 148 N - 67.1 N = 80.9 N. The acceleration can be found using Newton's second law, F = ma, so a = net force / m which gives us 80.9 N / 12 kg = 6.74 m/s².

The magnitude of the normal force can be found using mg cos(θ), which gives us 12 kg × 9.8 m/s² × cos(35°) = approximately 122.3 N.