A box (massm= 15kg) is placed on a slope (θ= 35◦), as shown in the diagram...

A box (massm= 15kg) is placed on a slope (θ= 35◦), as shown in the diagram below. Thecoefficients of friction between the box and the slope areμs= 0.6 andμk= 0.4. The box is released from reston the slope.(a) (2 points)Draw a free-body diagram for the box after it is released.(b) (8 points)Determine the acceleration of the box after it is released.

Solutions

Expert Solution

a)

Mg - Weight of the box, M being the mass.
N - Normal force on the box
Ff - Frictional force
- Angle of the slope.

b)
The net force on the box,
M * a = M * g * sin - Ff ...(1)
Equating the forces perpendicular to the ramp, M * g * cos = N
Ff = k * N
Here we have taken the coefficient of kinetic friction, k since the gravitational force along the ramp is greater than the static frictional force.
Ff = k * M * g * cos ...(2)

Substituting (2) in (1),
M * a = M * g * sin - k * M * g * cos
Dividing M,
a = g * sin - k * g * cos
= g * [sin - k * cos]
= 9.81 * [sin(35) - 0.4 * cos(35)]
= 2.41 m/s^2

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

For the curve r = 5sinθ, find the slope of the tangent line when θ =...

For the curve r = 5sinθ, find the slope of the tangent line when θ = π / 2.

Find the slope of the tangent line to the curve r = 1 + cos(θ) at...

Find the slope of the tangent line to the curve r = 1 + cos(θ) at θ =π/4. Note, you do NOT need to find the equation of the tangent line.

Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 1 + 2 cos θ, θ = π/3

Using R with a Normal(θ, 1) distribution: 28, 33, 22, 35, 31 lets estimate θ by...

Using R with a Normal(θ, 1) distribution: 28, 33, 22, 35, 31 lets estimate θ by minimizing residuals. Using the L2 norm squared; 1. What is the function sp(θ) we would like to minimize? 2. Graph sp(θ). 3. Using the Bisection Method find the Minimum Residual Estimator for θ correct, 2 dec. places. 4. If using Newton’s Method for this optimization problem, what is the refinement increment h(t)?

A box slides down a plank of length d that makes an angle of θ with...

A box slides down a plank of length d that makes an angle of θ with the horizontal as shown. μk is the kinetic coefficient of friction and μs is the static coefficient of friction. a) Enter an expression for the minimum angle θ (in degrees) the box will begin to slide. b) Enter an expression for the nonconservative work done by kinetic friction as the block slides down the plank. Assume the box starts from rest and θ is...

A 40 m long concrete box culvert (n = 0.012) will be laid on a slope...

A 40 m long concrete box culvert (n = 0.012) will be laid on a slope S = 0.001. The inlet will have a headwall parallel the embankment and the entrance will be beveled on three sides. What should be the width, b, of the culvert if D = 1 m TW = 1.1 m, Q = 1.8 m3/s, and the HW < 3.0 m. Assume that the outlet creates the maximum headwater for your solution.

C++ language, only math equation, no code. A Box on a slope slides under the following...

C++ language, only math equation, no code. A Box on a slope slides under the following force F = m*g*sin(theta) - 0.2v(t). Assume m = 1kg and g=10 and theta = 30'. We want to simulate the slide using dt = 0.1 second interval. This means update frame rate is 10 per second. Initial speed is 0. After 2 seconds we like to know what is the current position and speed of the box. We want to do this using...

A block is placed on a plane inclined at 35 degrees relative to the horizontal. If...

A block is placed on a plane inclined at 35 degrees relative to the horizontal. If the bloc k slides down the plane with an acceleration of magnitude g/3, determine the coefficient of the kinetic friction between the block and plane.

The particle shown below is at rest, where F = 35.0 N, and θ = 36.3°....

The particle shown below is at rest, where F = 35.0 N, and θ = 36.3°. Find the magnitudes of F1 and F2. F1 = F2 =

A plant is placed in a sealed box with sufficient air, water and sunlight for several...

A plant is placed in a sealed box with sufficient air, water and sunlight for several months. A chemical is added to the chamber that immediately adds electrons to all the oxygen in the chamber. Assume plants cannot perform fermentation. Also remember that gas diffuses freely across membranes and cell walls. Which of the following is most likely if the plant is left in the chamber the plant will die because it will be unable to do respiration the plant...

Subjects