A truck moving at 100 km /h carries a steel girder that rest on its wooden floor. what is the minimum time in which the truck can come to a stop without the girder moving forward ? The coefficient of static friction between steel and wood is 0.5.
To determine the minimum time in which the truck can come to a stop without the girder moving forward, we need to consider the forces acting on the girder.
First, let's identify the forces involved:
1. Gravity: The weight of the girder acts vertically downward.
2. Normal Force: The wooden floor exerts an upward force on the girder to counteract its weight.
3. Friction Force: The static friction between the steel girder and the wooden floor opposes the motion of the girder.
In order for the girder to remain stationary while the truck comes to a stop, the maximum static friction force must be greater than or equal to the force trying to move the girder forward. This force is given by the product of the coefficient of static friction (μs) and the normal force.
The normal force acting on the girder is equal to its weight since it is resting horizontally on the wooden floor.
Now, let's calculate:
1. Weight (Force due to gravity) = mass × acceleration due to gravity
The mass of the girder is not given, but let's assume it to be 1000 kg (just for calculation purposes).
Weight of the girder = 1000 kg × 9.8 m/s² (acceleration due to gravity) = 9800 N
2. Normal Force = Weight of the girder = 9800 N
3. Maximum static friction force = coefficient of static friction × Normal Force
Maximum static friction force = 0.5 × 9800 N = 4900 N
Since the static friction force is the only horizontal force acting on the girder, it should be equal to or greater than the force trying to move the girder forward, which is the force required to accelerate the girder.
The force required to accelerate an object can be calculated using Newton's second law of motion: force = mass × acceleration.
Assuming the maximum acceleration that the truck can provide is zero (since it's coming to a stop), the force required to accelerate the girder is also zero.
Therefore, the static friction force (4900 N) is greater than the force trying to move the girder forward (zero), and the girder remains stationary even when the truck comes to a stop.
Hence, the girder will not move forward, and there is no minimum time required for the truck to come to a stop without the girder moving forward.
Vi = (100,000/3600) meters/second
The rest is just like your earlier problems. Post your attempt please