A mass of 20 kg on a plane inclined at 40 degrees. A string attached to that mass goes up the plane, passed over a pullley and is attached to mass of 30 kg that hangs verticalyy. a) find the acceleration and it's dirction b) the tension in the string. Assume no friction.
I first drew the picture. How would I find the equation since F=ma doesn't include everything?
The pulling mass is 30g. The retarding force is 20g*sinTheta.
So pulling mass - retarding force = totalmass*acceleration.
Tension= 30g - 30*acceleration
To find the equation of motion for this system, we can start by considering the forces acting on each object.
For the mass of 20 kg on the inclined plane, there are two forces to consider - the gravitational force (mg) acting vertically downward and the component of the gravitational force acting parallel to the inclined plane, which is mg*sin(40°). This component of the gravitational force acts in the direction opposite to the motion.
For the hanging mass of 30 kg, the only force acting on it is the gravitational force (30g), which acts vertically downward.
Let's denote the acceleration of the system as "a", and the tension in the string as "T".
Now, applying Newton's second law (F = ma) to each of the masses:
For the mass on the inclined plane:
- The net force acting on it is T - mg*sin(40°), where mg*sin(40°) represents the retarding force.
- So, the equation for this mass becomes T - mg*sin(40°) = 20a (equation 1)
For the hanging mass:
- The net force acting on it is the tension T.
- So, the equation for this mass becomes T = 30g (equation 2)
To solve the system of equations, substitute the value of T from equation 2 into equation 1:
30g - mg*sin(40°) = 20a
Rearranging the equation, we get:
a = (30g - mg*sin(40°))/20
Now, we can plug in the values of g (acceleration due to gravity) and calculate the acceleration "a".
To find the tension in the string, we can substitute the value of "a" into equation 2:
T = 30g - 30a
Now, plug in the calculated value of "a" to determine the tension "T".