Question

A rightward force is applied to a 5kg object to move it across a rough surface at 2 m/s^2. The coefficient of friction between the object and the surface is 0.4. What is the force applied?

Answer 1

To determine the force applied to move the object across the rough surface, we need to consider the forces acting on the object and apply Newton's second law.

The forces acting on the object are:

1. Applied Force (Fa): This is the force applied to move the object to the right.
2. Weight (W): This is the force due to the object's mass and acts vertically downward.
3. Frictional Force (Ff): This is the force opposing the motion of the object and acts parallel to the surface.

Let's break down the forces and equations involved:

1. Weight (W): W = mg, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth). W = 5 kg × 9.8 m/s² = 49 N

2. Frictional Force (Ff): Ff = μN, where μ is the coefficient of friction and N is the normal force. In this case, the normal force is equal to the weight (N = W). Ff = 0.4 × 49 N = 19.6 N

3. Applied Force (Fa): This is the force we want to calculate. Fa - Ff = ma, where a is the acceleration. Fa - 19.6 N = 5 kg × 2 m/s² Fa - 19.6 N = 10 N Fa = 10 N + 19.6 N Fa = 29.6 N

Therefore, the force applied to move the object across the rough surface is 29.6 N.