A 78 kg bag of mortar mix is sitting in the back of a truck rounding a traffic circle of radius 27 m at a speed of 21 km/h. Using the truck's frame of reference, find the force of contact between the bag and the side of the truck. Assume that the floor at the back of the truck is frictionless.
To find the force of contact between the bag and the side of the truck, we need to consider the forces acting on the bag and apply the concept of centripetal force.
First, let's consider the forces acting on the bag. We have the weight of the bag, which can be calculated as the mass of the bag multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, the weight of the bag is given by:
Weight = mass x acceleration due to gravity
= 78 kg x 9.8 m/s^2
= 764.4 N
Next, we need to find the net force acting on the bag in the frame of reference of the truck. Since the truck is moving in a circle, there is a centripetal force acting towards the center of the circle. This force is provided by the frictional force between the bag and the side of the truck.
The centripetal force can be calculated using the formula:
Centripetal force = mass x (velocity^2 / radius)
Converting the speed from km/h to m/s:
Speed = 21 km/h x (1000 m/1 km) x (1 h/3600 s)
= 5.83 m/s
Note: To convert a quantity from km/h to m/s, multiply by (1000 m/1 km) and divide by (1 h/3600 s).
Now, substituting the values into the centripetal force formula:
Centripetal force = 78 kg x (5.83 m/s)^2 / 27 m
= 788.24 N
Since the frictional force between the bag and the side of the truck provides the necessary centripetal force, the force of contact between the bag and the side of the truck is equal to the centripetal force, which is 788.24 N.