Shortcut Methods and Tricks for Solving Numericals

Numerical - 1: A block of mass 10 kg is placed on a horizontal surface. A force of 20 N is applied to the block at an angle of 30° above the horizontal. The coefficient of kinetic friction between the block and the surface is 0.2. Find the acceleration of the block.

Shortcut Method:

1. Resolve the force F into its horizontal and vertical components.
2. Calculate the net force acting on the block in the horizontal and vertical directions.
3. Use Newton’s second law (F = ma) to find the acceleration of the block.

Numerical - 2: A car of mass 1200 kg is moving at a speed of 54 km/h on a horizontal road. The coefficient of static friction between the tires and the road is 0.7. What is the maximum braking force that can be applied to the car without causing it to skid?

Shortcut Method:

1. Calculate the maximum braking force that can be applied to the car without causing it to skid using the formula F = μs mg.

Numerical - 3: A block of mass 2 kg is placed on an inclined plane that makes an angle of 30° with the horizontal. The coefficient of kinetic friction between the block and the plane is 0.2. Find the acceleration of the block down the plane.

Shortcut Method:

1. Resolve the force of gravity acting on the block into its components parallel and perpendicular to the inclined plane.
2. Calculate the net force acting on the block in the parallel direction (down the plane).
3. Use Newton’s second law (F = ma) to find the acceleration of the block down the plane.