A box of mass 1kg is placed on a table and is connected to a hanging mass m by a string strung over a pulley. If the coefficient of kinetic friction between the box and the table is .3 and the box slides at a constant speed of .5m/s what is the weight of the hanging mass?
F_box=Fg of hanging mass
ma=mg
(1kg)a=m_hanging(9.8m/s^2)
But the problem is that i'm not given the acceleration of the 1kg box. How would i solve this problem?
To solve this problem, you can make use of the fact that the box is sliding at a constant speed of 0.5 m/s. When an object is moving at a constant speed, the net force acting on it is zero. In this case, the net force acting on the box is the force provided by the tension in the string (F_t) minus the force of friction (F_friction).
The tension in the string can be related to the weight of the hanging mass. Since the box is not accelerating, the tension in the string must be equal to the weight of the box (T = mg_box), which we can substitute as F_t = 1kg * 9.8m/s^2.
Similarly, the force of kinetic friction (F_friction) can be calculated using the coefficient of kinetic friction (μ_k) and the normal force (F_normal). The normal force is equal to the weight of the box (F_normal = mg_box), which we can substitute as F_friction = μ_k * F_normal.
Since the box is sliding at a constant speed, the force of kinetic friction must be equal in magnitude to the force provided by the tension in the string. Therefore, we have:
μ_k * F_normal = T
μ_k * mg_box = mg_box
μ_k = 0.3 (given)
Therefore, the weight of the hanging mass (mg_hanging) can be calculated as follows:
mg_hanging = m_hanging * 9.8m/s^2 = 0.3 * (1kg * 9.8m/s^2)
Solving this equation will give you the weight of the hanging mass.