A 3 meter tall 40 degree inclined plane with a coefficient of friction of .3 with a box sliding from its top has this acceleration and final velocity.
Initial PE= mg*3
frictionwork:mg*mu*Cos40*3/sin40
intialPE-workdonebyfriction=finalKE
two pint charges are 4 cm apart. They are moved to a new distance of 2 cm. By what factor does the resulting mutual forces between them change.
a. 1/2
b. 2
c. 1/4
d. 4
To determine the acceleration and final velocity of a box sliding down an inclined plane, you can use principles of physics such as Newton's second law and equations of motion.
First, let's calculate the component of the gravitational force pulling the box down the inclined plane. The force of gravity can be resolved into two components: one perpendicular to the plane and one parallel to the plane.
The component of gravity perpendicular to the plane is given by:
F_perpendicular = mass * acceleration due to gravity * cos(angle of inclination)
The component of gravity parallel to the plane is given by:
F_parallel = mass * acceleration due to gravity * sin(angle of inclination)
In this case, the angle of inclination is 40 degrees.
Next, let's calculate the force of friction acting on the box. The force of friction can be calculated using the equation:
F_friction = coefficient of friction * F_perpendicular
In this case, the coefficient of friction is given as 0.3.
Now, let's calculate the net force acting on the box. The net force is equal to the force parallel to the plane minus the force of friction:
Net force = F_parallel - F_friction
Once we have the net force, we can use Newton's second law, which states that force is equal to mass times acceleration:
Net force = mass * acceleration
Now, we have two equations with two unknowns, acceleration (a) and mass (m):
Net force = m * a
F_parallel - F_friction = m * a
Finally, using these equations, we can calculate the acceleration (a):
a = (F_parallel - F_friction) / m
Once you have the acceleration, you can use the equations of motion to calculate the final velocity of the box. Starting from rest (assuming the box starts from rest), we can use the equation:
v^2 = u^2 + 2as
where:
v = final velocity
u = initial velocity (which is 0 in this case)
a = acceleration (calculated above)
s = distance traveled down the incline (3 meters in this case)
Now, you can plug in the values and calculate the acceleration and the final velocity of the box sliding down the inclined plane.