In the figure below, we have a force \( F = 40 \, \text{N} \) pushing a box up an inclined plane with an angle \( \theta = 30^\circ \). The box has a mass \( m = 4 \, \text{kg} \), the coefficient of kinetic friction between the box and the inclined plane is \( \mu_k = 0.5 \), and the block moves a distance \( d = 10 \, \text{m} \) up the inclined plane.a) What is the work done by the force \( F \)? **Answer:** 400 J.b) What is the normal force from the inclined plane? **Answer:** 33.9 N.c) What is the work done by the kinetic friction force? **Answer:** -169.5 J.d) What is the work done by the gravitational force? **Answer:** -196 J.e) What is \( W_{\text{net}} \), the net work done on the box? **Answer:** 34.5 J.f) The box starts from rest. What is the speed of the box after it has travelled the distance \( d = 10 \, \text{m} \) up the incline plane? **Answer:** 4.2 m/sec.The diagram shows a box on an inclined plane angled at \( 30^\circ \) with a force of 40 N applied parallel to the incline. The box's mass is 4 kg, and the kinetic friction coefficient is 0.5. The image contains equations related to work in physics:\[ W = F_{\parallel} \Delta x = \vec{F} \cdot \Delta \vec{x} \]This equation represents the work done \( W \) by a force \( F \) that is parallel to the displacement \( \Delta x \). It can also be expressed as the dot product of the force vector \( \vec{F} \) and the displacement vector \( \Delta \vec{x} \).\[ W_{\text{net}} = \frac{1}{2} m (v_f)^2 - \frac{1}{2} m (v_i)^2 \]This relates the net work \( W_{\text{net}} \) to the change in kinetic energy of an object, where \( m \) is the mass, \( v_f \) is the final velocity, and \( v_i \) is the initial velocity.\[ W = \int F_x \, dx \]This integral represents the work done when a varying force \( F_x \) acts along the x-axis over a distance.\[ W = \int \vec{F} \cdot d\vec{r} \]This integral represents the work done by a force \( \vec{F} \) along a path, where \( d\vec{r} \) is an infinitesimal displacement vector.These equations explore the concept of work done by forces on an object and relate it to displacement and energy changes.

Name: In the figure below, we have a force \( F = 40 \, \text{N} \) pushing
Uploaded: 2024-03-20T06:57:25.000Z
Channel: Bartleby
Description: In the figure below, we have a force \( F = 40 \, \text{N} \) pushing a box up an inclined plane with an angle \( \theta = 30^\circ \). The box has a mass \( m = 4 \, \text{kg} \), the coefficient of kinetic friction between the box and the inclined