In Fig. 6-24, a force P⃗ acts on a block weighing 45 N . The block is initially at rest on a pla

step 1 First going to apply Newton's second law in the Y direction. We can say the sum of forces in the

In Fig. 6-24, a force P⃗ acts on a block weighing 45 N . The...

In Fig. $6-24,$ a force $\vec{P}$ acts on a block weighing 45 $\mathrm{N}$ . The block is initially at rest on a plane inclined at angle $\theta=15^{\circ}$ to the horizontal. The positive direction of the $x$ axis is up the plane. Between block and plane, the coefficient of static friction is $\mu_{s}=0.50$ and the coefficient of kinetic friction is $\mu_{k}=0.34 .$ In unit-vector notation, what is the frictional force on the block from the plane when $$\vec{P}$ is (a) $(-5.0 \mathrm{N}) \hat{\mathrm{i}},(\mathrm{b})(-8.0 \mathrm{N}) \hat{\mathrm{i}},$ and $(\mathrm{c})(-15 \mathrm{N}) \hat{\mathrm{i}} ?$$

In Fig. $6-24,$ a force $\vec{P}$ acts on a block weighing 45 $\mathrm{N}$ . The block is initially at rest on a plane inclined at angle $\theta=15^{\circ}$ to the horizontal. The positive direction of the $x$ axis is up the plane. Between block and plane, the coefficient of static friction is $\mu_{s}=0.50$ and the coefficient of kinetic friction is $\mu_{k}=0.34 .$ In unit-vector notation, what is the frictional force on the block from the plane when
$$\vec{P}$ is (a) $(-5.0 \mathrm{N}) \hat{\mathrm{i}},(\mathrm{b})(-8.0 \mathrm{N}) \hat{\mathrm{i}},$ and $(\mathrm{c})(-15 \mathrm{N}) \hat{\mathrm{i}} ?$$

Key Concepts

Static Friction

Static friction is the resistance to the initiation of motion between two surfaces in contact. It acts in the direction opposite to the potential motion and adjusts up to a maximum value, determined by the normal force multiplied by the coefficient of static friction, to prevent motion when forces are applied.

Kinetic Friction

Kinetic friction is the force that opposes the relative motion between surfaces already sliding against each other. Its magnitude is typically smaller than the maximum static friction and is given by the product of the kinetic friction coefficient and the normal force.

Force Decomposition on an Inclined Plane

When analyzing forces on an inclined plane, it is important to decompose vectors (such as gravity or an applied force) into components parallel and perpendicular to the plane. This allows for the proper calculation of forces acting along the direction of potential motion (or equilibrium) and those affecting the normal force.

Free-Body Diagram Analysis

A free-body diagram is a visual tool used to represent all the forces acting on an object. In the context of an inclined plane, it typically includes the gravitational force, normal force, frictional force, and any applied forces. This diagram is essential for setting up the equations of motion or equilibrium.

Unit Vector Notation

Unit vector notation is a method of expressing vectors in terms of their direction along predefined axes. It allows for clear representation of vector components, which is particularly useful when decomposing forces into parallel and perpendicular components relative to a surface, such as an inclined plane.

Transcript

Please give Ace some feedback