An object of mass M rests on a horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m. There is static friction between the horizontal surface and mass M.
The coefficient of static friction is 0.75 and M=15. kg.
The string and pulley are ideal and massless. Use g=9.8 m/s2.
What is the maximum value of mass m that can be hung from the strong so that mass M does not slide on the surface?
mass m is the pulling force, mg
M is being pulled, a maximum of Mg*mu
mg<=Mg*mu
To find the maximum value of mass m that can be hung from the string so that mass M does not slide on the surface, we need to consider the forces acting on the system.
1. Calculate the maximum static friction force (Fmax):
The maximum static friction force (Fmax) can be calculated using the formula: Fmax = μs * N, where μs is the coefficient of static friction and N is the normal force.
In this case, the normal force (N) is equal to the weight of mass M, which can be calculated as N = M * g.
2. Set up equations for the forces:
Write the equation for the forces acting on mass M in the horizontal direction:
Fnet = T - Fmax = 0
where T is the tension in the string.
Write the equation for the forces acting on mass m in the vertical direction:
Fnet = m * g - T = 0
3. Solve the system of equations:
Rearrange the equations to solve for T:
T = Fmax and T = m * g
Set both equations equal to each other:
Fmax = m * g
Substitute the value of Fmax:
μs * N = m * g
Substitute the values of μs, N, and g:
0.75 * (15 kg * 9.8 m/s^2) = m * 9.8 m/s^2
Simplify and solve for m:
11.025 kg = m
Therefore, the maximum value of mass m that can be hung from the string so that mass M does not slide on the surface is approximately 11.025 kg.