A crate is initially at rest and then slides down a long inclin that is 30 degrees above the horizontal. If the coefficient of kinetic friction is 0.40, the speed of the crate after 5s is ?
force down the plane=mgSinTheta
friction force up plalne=mu*mgCosTheta
netforce=ma
mg(sinTheta-mu*CosTheta)=ma
solve for a.
then, vf=a*time=5a
To find the speed of the crate after 5 seconds, we can use the principles of physics and break down the problem step by step.
First, let's consider the forces acting on the crate. There are two main forces to consider: the gravitational force pulling the crate down the incline and the frictional force opposing the motion of the crate. Since the crate is sliding down the incline, the frictional force will be in the opposite direction of the motion.
The force of gravity can be split into two components: the component parallel to the incline and the component perpendicular to the incline. The component parallel to the incline is given by mg * sin(θ), where m is the mass of the crate, g is the acceleration due to gravity, and θ is the angle of the incline.
The frictional force can be calculated by multiplying the coefficient of kinetic friction (μk) by the normal force, which is the force perpendicular to the incline. The normal force is given by mg * cos(θ).
Now, let's apply Newton's second law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the force parallel to the incline minus the frictional force.
Therefore, we have the following equation of motion for the crate:
(mg * sin(θ) - μk * mg * cos(θ)) = m * a
Where a is the acceleration of the crate.
To find the acceleration, we need to solve the equation for a. Rearranging the equation, we get:
a = (g * sin(θ) - μk * g * cos(θ))
Plugging in the given values, we have:
a = (9.8 m/s^2 * sin(30 degrees) - 0.40 * 9.8 m/s^2 * cos(30 degrees))
Calculate the values, and we find:
a ≈ 4.9 m/s^2
Now, to find the speed of the crate after 5 seconds, we can use the equation of motion:
v = u + a * t
Where v is the final velocity, u is the initial velocity (which is zero in this case), a is the acceleration, and t is the time.
Plugging in the values:
v = 0 + 4.9 m/s^2 * 5 s
Solving the equation, we get:
v ≈ 24.5 m/s
Therefore, the speed of the crate after 5 seconds is approximately 24.5 m/s.