How to Calculate Speed and Height in Physics Mechanics Problems
Understanding the Physics Mechanics Problem
How can we determine the speed of each object when they pass each other and when the 5.35-kg object hits the table?
What is the calculation for how much higher the 2.95-kg object travels after the 5.35-kg object hits the table?
Final answer:
The object's speed is given by v = sqrt(2ah) when they pass each other and when the 5.35-kg object hits the table. The higher the 2.95-kg object travels after the 5.35-kg hits the table can be calculated by equating the kinetic energy it possessed at the instant the 5.35 Kg mass hits the ground, to the potential energy, so mgh = 1/2 mv².
Explanation:
This scenario is essentially a problem of physics, specifically dealing with mechanics. The objects in question are connected by a light string passing over a light, frictionless pulley, so they are a 2-body system in free fall. Consequently, the conservation of energy and Newton's second law, F=ma, or equivalently the law of acceleration a = F/m, are applicable here.
(a) Both the objects will be accelerated at the same rate regardless of their mass. The acceleration is given by a = (m1 - m2)g / (m1+ m2), where g is the acceleration due to gravity, which is 9.81 m/s². Substituting the given values will give you a. Then, The speed of the objects when they pass each other can be determined using the equation v² = u² + 2as, since the objects start from rest (initial velocity, u, is zero), so v = sqrt(2ah), where h is the height.
(b) The speed of each object when the 5.35-kg object hits the table will be same as part (a).
(c) Now Consider the system at the instant when the 5.35 Kg mass hits the ground. At that point, it will stop exerting a force on the 2.95 Kg mass but the 2.95 Kg mass would have attained some speed due to earlier acceleration. This will cause it to move higher, even after the other block hits the ground. The height can be calculated by transforming the kinetic energy it possessed when the other block hit the ground to potential energy. So, mgh = 1/2 mv², and you can solve for h.