A CART OF MASS 20 KG AT REST IS TO BE DRAGGED AT A SPEED OF 18 KM/HR. IF COEFFICIENT OF FRICTION IS 0.1, WHAT IS THE MINIMUM FORCE REQUIRED TO DRAG CART TO A DISTANCE OF10 METRES. TAKE g=10 m/s^2

To determine the minimum force required to drag a cart with a mass of 20 kg at a speed of 18 km/h over a distance of 10 meters, we need to consider the forces acting on the cart, particularly the force of friction. Let's break this down step by step.

Understanding the Forces Involved

When dragging the cart, the primary opposing force is friction, which can be calculated using the formula:

• Frictional Force (F_friction) = μ × N

Here, μ is the coefficient of friction, and N is the normal force. For a horizontal surface, the normal force is equal to the weight of the cart, which can be calculated as:

• N = m × g

Where:

• m = mass of the cart = 20 kg
• g = acceleration due to gravity = 10 m/s²

Calculating the Normal Force

Substituting the values into the equation for normal force:

• N = 20 kg × 10 m/s² = 200 N

Calculating the Frictional Force

Now, using the coefficient of friction (μ = 0.1):

• F_friction = 0.1 × 200 N = 20 N

Determining the Minimum Force Required

The minimum force required to drag the cart must overcome this frictional force. Therefore, the minimum force (F_min) needed is:

• F_min = F_friction = 20 N

Considering the Speed

It's important to note that the speed of 18 km/h (which is equivalent to 5 m/s) does not directly affect the minimum force required to overcome friction in this scenario. The force calculated is sufficient to maintain that speed as long as it overcomes the frictional force.

Summary of the Calculation

To summarize, the minimum force required to drag the cart a distance of 10 meters at a speed of 18 km/h, given a coefficient of friction of 0.1, is:

• 20 N

This force will allow you to maintain the desired speed while overcoming the friction acting against the motion of the cart. If you have any further questions or need clarification on any part of this process, feel free to ask!