A block of mass M is pulled with a force F along a smooth horizontal surface with a rope of mass m. The acceleration of the block will be given by,
Does it only need the formula? If so acceleration would be a= F/m where F = Force and m = mass
the rope has to accelerate too, so a = F/(M+m)
To determine the acceleration of the block when pulled with a force along a smooth horizontal surface, we can apply Newton's second law of motion.
According to Newton's second law, the acceleration (a) of an object is directly proportional to the net force (Fnet) acting on it and inversely proportional to its mass (m).
Mathematically, we can express this relationship as:
Fnet = ma
In this scenario, we have a block of mass M being pulled with a force F along a smooth surface. Let's assume that the mass of the rope is m.
The net force acting on the block can be calculated by subtracting the force due to the inertia of the rope from the applied force:
Fnet = F - F_inertia
The force due to the inertia of the rope can be calculated by multiplying the mass of the rope (m) by the acceleration of the rope (a):
F_inertia = ma
Substituting this back into the equation for net force:
Fnet = F - ma
Now, we can rearrange the equation to solve for acceleration (a):
a = (F - F_inertia)/M
Substituting F_inertia = ma:
a = (F - ma)/M
This is the equation that describes the acceleration of the block when pulled with a force along a smooth horizontal surface.