A worker can supply a maximum pull of 150 lbs. on a cart which has a handle set an angle of 40degree above the horizontal. what is the coefficient of friction if he can just move a total load of 1500lbs. ?

Normal force at maximum moveable load

= 1500 - 150sin40 = 1404 lb

Coefficient of friction (static)
= (tangential force)/(normal force)
= 1500 cos40/1404 = 0.818

To determine the coefficient of friction, we need to analyze the forces acting on the cart.

Let's break down the forces:

1. The worker's maximum pull force: 150 lbs.
2. The weight of the load: 1500 lbs.
3. The normal force (perpendicular to the surface of the cart).

Now, let's analyze the forces vertically:

The weight of the load (1500 lbs.) acts downward, and the normal force acts upward. Since the cart is on a horizontal surface, the normal force is equal in magnitude and opposite in direction to the weight of the load, i.e., 1500 lbs.

Next, let's analyze the forces horizontally:

Since the handle of the cart is set at an angle of 40 degrees above the horizontal, we need to resolve the maximum pull force (150 lbs.) into its horizontal and vertical components.

The horizontal component of the maximum pull force is given by:

Horizontal component = Maximum pull force * cos(angle)
Horizontal component = 150 lbs * cos(40°)

Therefore, the horizontal component of the maximum pull force is:

Horizontal component = 150 lbs * cos(40°) = 114.99 lbs (approximately 115 lbs)

Now that we have the horizontal component of the maximum pull force, we can determine the frictional force acting on the cart. The frictional force is given by:

Frictional force = Coefficient of friction * Normal force

We know that the Frictional force equals the Horizontal component of the maximum pull force:

Frictional force = 115 lbs

So, we can write:

Coefficient of friction * 1500 lbs = 115 lbs

Therefore, the coefficient of friction is:

Coefficient of friction = 115 lbs / 1500 lbs

Simplifying this equation gives us the coefficient of friction:

Coefficient of friction = 0.0767 (approximately 0.08)

Hence, the coefficient of friction is approximately 0.08.

To find the coefficient of friction, we can use the given information and the concept of force equilibrium. The worker can exert a maximum pull of 150 lbs., and the angle of the handle is 40 degrees above the horizontal.

First, let's break down the forces acting on the cart:

1. Pulling Force (Fp): This is the force exerted by the worker and is given as 150 lbs.
2. Normal Force (N): This is the force perpendicular to the contact surface between the cart and the ground. We can assume it is equal to the weight of the cart, which is 1500 lbs.
3. Frictional Force (Ff): This is the force opposing the motion of the cart.

We need to find the coefficient of friction (μ) in this scenario. The formula for frictional force is given by:

Ff = μN

To determine the maximum force of friction, we consider the force components acting parallel to and perpendicular to the inclined surface.

1. Parallel Component of Weight (Wp): The weight of the cart can be broken down into components acting parallel and perpendicular to the incline. The parallel component can be calculated as follows:

Wp = mg sin(θ)

Where m is the mass of the cart and g is the acceleration due to gravity (approximately 32 ft/s²).

2. Force Parallel to the Incline (Fp'): This force is the parallel component of the pulling force Fp acting in the same direction as the motion:

Fp' = Fp sin(θ)

Where θ is the angle of the handle set above the horizontal.

The force equilibrium equation for the cart in the horizontal direction is:

Fp' - Ff = 0

Now, substitute the values into the equation:

150 lbs * sin(40°) - Ff = 0

Solving for Ff:

Ff = 150 lbs * sin(40°)

Finally, we can substitute Ff into the frictional force equation:

μN = Ff

μ * (1500 lbs) = 150 lbs * sin(40°)

Solving for μ:

μ = (150 lbs * sin(40°)) / (1500 lbs)

Calculating this, we find:

μ ≈ 0.173

Therefore, the coefficient of friction (μ) in this scenario is approximately 0.173.