Assume there is a large frictional force acting on the cart (coefficients of friction ðð = 0.4 and ðð = 0.15), and the total mass ð = ð1 + ð2 = 0.65ðð.
a. Find the equation for the acceleration of the cart in terms of ðð, the masses, and g â assuming that the cart is moving along the track.
net force=mass*a
pushing force-friction= M ( acceleration)
pushing force-uk*M*g=M*acceleration
solve for acceleration.
To find the equation for the acceleration of the cart, we need to consider the forces acting on it. In this case, there are two forces to consider: the force due to friction and the force due to gravity.
1. Force due to friction:
The frictional force can be calculated using the equation:
Frictional force = coefficient of friction * Normal force
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is equal to the weight of the cart (ðg).
So, the frictional force can be calculated as:
Frictional force = ðð * ðg
2. Force due to gravity:
The force due to gravity is equal to the weight of the cart (ðg), where g is the acceleration due to gravity.
Now, let's consider Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Net force = mass * acceleration
Since the frictional force and the force due to gravity act in opposite directions, we need to subtract the frictional force from the force due to gravity to get the net force:
Net force = ðg - Frictional force
Substituting the values for the frictional force and the net force into the equation, we get:
ðg - ðð * ðg = ð * acceleration
Now, we can simplify the equation:
ð(1 - ðð) * g = ð * acceleration
Finally, we cancel out the mass term from both sides of the equation:
(1 - ðð) * g = acceleration
So, the equation for the acceleration of the cart in terms of ðð, the masses, and g is:
acceleration = (1 - ðð) * g