a 4kg box sits, at rest,on the table what is the box's acceleration? b)how much does the box weight? c) what other force acts on the box? how big is this force?
If it is "at rest" that implies it is sitting there not moving therefor not accelerating. Weight is simply mass x gravity (W=mg) where g~9.81(m/s^2). Newtons Second law Net Force = mass x acceleration (F=ma) reveals if the box has a downward force of W, and is not moving, there must be an equal but opposite force to hold it here. The table exerts this force commonly called N. So if F=ma and a is zero n-mg=0 so n=mg.
To find the answers to these questions, we need to understand the basic concepts of Newton's laws of motion.
a) The box is at rest on the table, indicating that there is no net force acting on it. According to Newton's first law of motion (also known as the law of inertia), an object at rest tends to stay at rest unless acted upon by an external force. Since the box is not moving, its acceleration is zero.
b) Weight refers to the force of gravity acting on an object. The weight of an object can be calculated using the formula:
Weight = mass × acceleration due to gravity
Given that the box has a mass of 4 kg, we can calculate its weight by multiplying its mass by the acceleration due to gravity. The standard acceleration due to gravity on Earth is approximately 9.8 m/s^2:
Weight = 4 kg × 9.8 m/s^2 = 39.2 N
Therefore, the box weighs 39.2 Newtons.
c) The other force acting on the box is the force of the table pushing upward. This force, known as the normal force, is exerted by the table to support the weight of the box. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So, the normal force exerted by the table on the box is equal in magnitude but opposite in direction to the weight of the box.
Since the weight of the box is 39.2 N, the normal force exerted by the table is also 39.2 Newtons.
In summary:
a) The box's acceleration is zero.
b) The box weighs 39.2 Newtons.
c) The force acting on the box is the normal force, whose magnitude is also 39.2 Newtons.