An 8.00 kg box sits on a ramp that is inclined at 33.0^∘ above the horizontal. The coefficient

step 1 All right, hello. In this question, we're given the setup. We have a block on a ramp. We're give

An 8.00 kg box sits on a ramp that is inclined at 33.0^∘...

An $8.00 \mathrm{~kg}$ box sits on a ramp that is inclined at $33.0^{\circ}$ above the horizontal. The coefficient of kinetic friction between the box and the surface of the ramp is $\mu_{\mathrm{k}}=0.300 .$ A constant horizontal force $F=26.0 \mathrm{~N}$ is applied to the box (Fig. $\mathbf{P} 5.73$ ), and the box moves down the ramp. If the box is initially at rest, what is its speed $2.00 \mathrm{~s}$ after the force is applied?

Key Concepts

Kinematics

Kinematics involves the equations of motion that relate displacement, velocity, acceleration, and time. When an object starts from rest and undergoes constant acceleration, kinematic equations help determine its speed after a given time interval.

Kinetic Friction

Kinetic friction is the resistive force that acts opposite the direction of motion when an object is sliding over a surface. It is calculated using the normal force and the coefficient of kinetic friction, and it plays a crucial role in determining the net acceleration of objects on inclined planes.

Newton's Second Law

Newton's Second Law, expressed as F_net = m*a, is the principle that the net force acting on an object is equal to its mass times its acceleration. This law is central to solving for the acceleration of an object when multiple forces, including friction and applied forces, are acting on it.

Inclined Plane Dynamics

This concept deals with the motion of objects on a sloped surface. It involves understanding how gravity is subdivided into components that are parallel and perpendicular to the plane, which is essential for analyzing motion and forces acting along the inclined surface.

Force Decomposition

Force decomposition involves breaking a force into its components along chosen axes. For objects on an incline, forces such as gravity or an applied horizontal force must be resolved into components that are parallel and perpendicular to the surface to accurately calculate net forces and predict motion.

Transcript

0:00 All right, hello.

00:01 In this question, we're given the setup.

00:01 We have a block on a ramp.

00:03 We're given the incline and the mass of the block as 8 kilograms.

00:06 And we're asked, after 2 seconds, if it starts from rest, so if v0 is equal to 0, after 2 seconds, how fast is this block going to be moving? so what is vfinal going to be? if i find my acceleration, i can use the definition of acceleration, which is some change in speed over change in time, to help find vfinal.

00:24 So i just need to figure out what my acceleration is here.

00:27 In order to do that, i'm going to need to draw the rest of this free body diagram.

00:30 So i'm going to have my weight pushing down.

00:32 I'm going to have my normal force, normal to the surface.

00:35 And it's going to be sliding down.

00:36 So i'm going to have some force of friction, because i have some constant of kinetic friction here.

00:43 And that's going to be opposing that motion.

00:45 And i'm going to choose my axes like so.

00:47 I'm going to have plus x down the ramp and plus y normal to the ramp.

00:51 If i do a sum of the forces in the y direction, i'll have my normal force.

00:54 And then i also have a component of my applied force.

00:57 So i have my applied force, but just in the y direction.

01:00 Well, how does that relate to theta? if i draw a parallel line going here, that is going to be my angle of theta there.

01:08 And so my y component of the force is going to be f times the sine of theta.

01:13 And then the opposite direction, pushing down, i have a component of my weight.

01:17 So i can break my weight down in that way.

01:18 And this angle here is going to be theta...

Please give Ace some feedback