Calculate the maximum speed at which the cargo rounds the bend without skidding if the coefficient of friction between the tyre an the ground is 0.5?

To calculate the maximum speed at which the cargo rounds the bend without skidding, we can use the formula for centripetal force. This force is responsible for keeping the cargo moving in a circular path around the bend.

The centripetal force, Fc, is given by the equation:

Fc = mv² / r

Where:
- m is the mass of the cargo
- v is the velocity of the cargo
- r is the radius of the bend

In this case, we want to find the maximum speed at which the cargo can go without skidding. Skidding occurs when the centripetal force exceeds the maximum possible friction force. The maximum friction force, Ff (or Fmax), is given by the equation:

Ff = μN

Where:
- μ is the coefficient of friction between the tire and the ground (0.5 in this case)
- N is the normal force acting on the tire

Since the cargo is rounding a bend, the normal force, N, can be calculated as the weight of the cargo, mg.

Combining the equations for the centripetal force and the maximum friction force, we have:

Fc = Ff

mv² / r = μN

mv² / r = μmg

Simplifying the equation:

v² = μgr

Now, we can solve for the maximum velocity, v:

v = √(μgr)

Plugging in the values:

v = √(0.5 * 9.8 * r)

The value of "r" (the radius of the bend) is not provided in the question, so you need to determine the radius of the bend first. Once you have the radius, substitute it in the equation above to find the maximum speed at which the cargo can round the bend without skidding.