A boy is moving on a straight road against a frictional force of 5 N. After travelling a distance of 1.5 km he forgot the correct path at a round about of radius 100 m. However, he moves on the circular path for one and half cycle and then he moves forward upto 2 km. Calculate the work done by him.
is the 200 m distance across the round about part of the 2 km?
No
To calculate the work done by the boy, we need to consider the work done against the frictional force and the work done when moving on the circular path.
1. Work done against the frictional force:
The work done is given by the formula: work = force × distance
In this case, the frictional force is 5 N and the distance travelled in a straight line is 1.5 km.
However, to calculate the work done only against the frictional force, we need to find the component of the distance travelled in the direction opposite to the force. Since the boy is moving against the frictional force, the work done is negative.
Therefore, the work done against the frictional force is: work = -5 N × 1.5 km
2. Work done on the circular path:
To find the work done on the circular path, we need to calculate the force exerted by the boy and the distance travelled on the circular path.
The force exerted by the boy can be found using Newton's second law: force = mass × acceleration. However, since the mass is not given in the question, we need to find an alternative approach.
We know that the net force acting on an object moving in a circular path is given by the centripetal force.
The centripetal force is given by the formula: force = (mass × velocity^2) / radius
Here, the velocity can be calculated using the distance travelled on the circular path and the time taken to complete one and a half cycles.
Given that the roundabout's radius is 100 m and the boy moves on the circular path for one and a half cycles, we can calculate the circumference of the circular path.
Circumference of a circle = 2π × radius
Distance travelled on the circular path = circumference × 1.5
Once we have the distance travelled on the circular path, we can calculate the time taken using the relation: velocity = distance / time.
Knowing the velocity, we can calculate the centripetal force using the above formula.
Now, once we have the force and the radius of the circular path, we can calculate the work done on the circular path using the formula: work = force × distance.
3. Work done on the straight road:
Finally, to calculate the work done on the straight road, we need to use the formula: work = force × distance.
Here, the force is the resultant force acting on the boy, which can be calculated by using the Pythagorean theorem: force^2 = (force against friction)^2 + (centripetal force)^2.
The distance travelled on the straight road is given as 2 km.
Adding all the work done components will give us the total work done by the boy.