A mass m1 = 18.7 kg on a frictionless ramp is attached to a light string. The string passes over a frictionless pulley and is attached to a hanging mass m2. The ramp is at an angle of θ = 23.7° above the horizontal. m1 moves up the ramp uniformly (at constant speed). Find the value of m2.
Let tension in string = T
m2 g = T since there is no acceleration
now draw forces on m1 up and down ramp
T = up ramp force
m1 g sin 23.7 = force down ramp
net force up ramp = m1 a = 0
so
T = m1 g sin 23.7
so
m2 g = m1 g sin 23.7
m2 = m1 sin 23.7
unit of measurement required??? waht is answer exactly of m2??
mass of m1 is given in kg
so m2 is in kg
now I am sure you can do 18.7 * sin 23.7
thanks a lotttttttt
To find the value of m2, we can use the principles of Newton's second law and the concept of equilibrium.
First, let's analyze the forces acting on the system. For mass m1 on the ramp, we have the gravitational force (mg) acting downward and the normal force (N) acting perpendicular to the ramp. Additionally, there is tension (T) in the string pulling m1 up the ramp, as well as the weight of m2 hanging vertically.
In the equilibrium condition, the sum of the forces in the horizontal direction and the sum of the forces in the vertical direction should both be equal to zero.
Horizontal forces:
The only horizontal force in this case is the component of tension (T) parallel to the ramp. Since there is no friction, this force must be equal and opposite to the component of gravitational force acting parallel to the ramp (mg*sinθ).
T*cosθ = mg*sinθ
Vertical forces:
In the vertical direction, we have the component of gravitational force acting perpendicular to the ramp (mg*cosθ), the normal force (N), and the weight of m2 (m2*g).
N - mg*cosθ - m2*g = 0
Since m1 moves up the ramp at a constant speed, the net force acting on m1 is zero. Therefore, the tension (T) in the string must be equal to mg*sinθ.
T = mg*sinθ
Now, we can substitute the value of T in terms of mg*sinθ into the equation for the horizontal forces:
mg*sinθ*cosθ = mg*sinθ
By canceling out mg*sinθ on both sides of the equation, we get:
cosθ = 1
As the cosθ = 1, we can conclude that cosθ = 1.
Thus, the ramp is horizontal, and no mass m2 is needed to keep mass m1 moving at a constant speed up the frictionless ramp.