A 0.700 kg object attached to the end of a 0.560 meter wire revolves uniformly on a flat, frictionless surface.
a) If the object makes three complete revolutions per second, what is the force exerted by the wire on the object?
b) What is the speed of the object?
To answer these questions, we need to understand the concept of centripetal force and the relationship between speed and centripetal force.
a) The force exerted by the wire on the object is the centripetal force, which keeps the object moving in a circular path. The centripetal force is given by the equation:
Fc = (m * v^2) / r
where Fc is the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path.
In this case, the object makes three complete revolutions per second, which means it completes three circles in one second. To find the velocity of the object, we can multiply the circumference of the circle by the number of circles per second:
v = 2πr * 3
Since the radius of the circle is given as 0.560 meters, we can substitute this value into the equation to find the velocity.
Once we have the velocity, we can substitute the values of mass (0.700 kg) and radius (0.560 meters) into the equation to find the force exerted by the wire on the object.
b) The speed of the object can be calculated using the formula:
v = (2πr * n)
where v is the speed of the object, r is the radius of the circular path, and n is the number of revolutions per second.
You already have the value of r (0.560 meters) and n (3 revolutions per second). By substituting these values into the equation, you can find the speed of the object.
Now that we have explained the process, you can go ahead and calculate the answers to these questions.