A 30 kg student pushes a 20kg box on frictionless surface. If student accelerates at 0.8m/s^2(N),what is acceleration of bix. now why does the box acceerate towards south, if it is being pushed north should it not move north.
Before the push, the momentum of the system was zero
so since there is no EXTERNAL force on the student/box system,
After the push the total momentum of the system is zero.
Therefore
If the student goes North
then
The box goes South
if north is +
.8 (30) + v (20) = 0
v = -.8(30/20)
PS
Perhaps you missed that word "frictionless"
Do not think you are pushing that box along a hockey rink. That requires friction and cleats on your shoes if on ice.
If no cleats, if the box goes one way you go the other :)
The answer would be 1.2 m/s^2.
Since the student is pushing against the box, the amount of force they are using is equivalent to the amount of force the box is pushing back (As explained by Newton's third law of motion). Therefore, you first have to find the amount of force the student is using, and then set that equal to the mass of the box to find its acceleration.
F(of the student)=ma
=30(.8)
=24N
F(student)=f(box)
24N=ma
24=20(a)
acceleration of the box= 24/20= 1.2 m/s^2
To find the acceleration of the box, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
The force exerted by the student on the box is the product of the mass of the student and the acceleration of the student, given by:
Force = mass_student * acceleration_student
Using the given values:
mass_student = 30 kg
acceleration_student = 0.8 m/s^2
Force = 30 kg * 0.8 m/s^2
Force = 24 N
Since there are no other horizontal forces acting on the box, the force of 24 N applied by the student is the only force causing the acceleration of the box.
Now, considering the direction of the acceleration of the box. It's important to note that the direction of acceleration is determined by the net force acting on the object, not the direction the object is being pushed.
In this case, the student is pushing the box towards the north, which means the applied force is directed towards the north. However, since there is no friction or any other external force acting in the opposite direction, the net force on the box is also towards the north.
As a result, the box accelerates towards the north, in the same direction as the applied force. The box does not accelerate towards the south.