Question

A box with 10 kg of mass slides down an inclined plane that is 1.7 m...

A box with 10 kg of mass slides down an inclined plane that is 1.7 m high and 3.5 m long. Due to friction the box reaches 3.0 m/s at the bottom of the inclined plane. Beyond the inclined plane lies a spring with 650 N/m constant. It is fixed at its right end. The level ground between the incline and the spring has no friction

The box compressed the spring, got pushed back towards the incline by the spring. How far along the inclined plane, from the bottom, will the box temporarily stop on the inclined plane?

Homework Answers

Answer #1

here,

mass of box , m = 10 kg

height of incline , h1 = 1.7 m

s1 = 3.5 m

theta = arcsin(h1/s1) = 29.1 degree

v = 3 m/s

let the friction force acting be ff

using Work energy theorm

m * g * h1 - ff * s1 = 0.5 * m * v^2

10 * 9.81 * 1.7 - ff * 3.5 = 0.5 * 10 * 3^2

solving for ff

ff = 34.8 N

when the block moves up the incline

let the block traveles s2 m before temporarily stop

using Work energy theorm

- m * g * s2 * sin(theta) - ff * s2 = (0 - 0.5 * m * v^2)

10 * 9.81 * s2 * sin(29.1) + 34.8 * s2 = 0.5 * 10 * 3^2

solving for s2

s2 = 0.55 m

the block traveles 0.55 m before temporarily stop

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A box with 11 kg of mass slides down an inclined plane that is 2.0 m...
A box with 11 kg of mass slides down an inclined plane that is 2.0 m high and 3.5 m long. Due to friction the box reaches 3.3 m/s at the bottom of the inclined plane. Beyond the inclined plane lies a spring with 650 N/m constant. It is fixed at its right end. The level ground between the incline and the spring has no friction The box compressed the spring, got pushed back towards the incline by the spring....
A block of mass m = 3.3 kg is on an inclined plane with a coefficient...
A block of mass m = 3.3 kg is on an inclined plane with a coefficient of friction μ1 = 0.39, at an initial height h = 0.53 m above the ground. The plane is inclined at an angle θ = 44°. The block is then compressed against a spring a distance Δx = 0.13 m from its equilibrium point (the spring has a spring constant of k1 = 35 N/m) and released. At the bottom of the inclined plane...
A 4.25 kg block is projected at 5.40 m/s up a plane that is inclined at...
A 4.25 kg block is projected at 5.40 m/s up a plane that is inclined at 30.0° with the horizontal. The block slides some distance up the incline, stops turns around and slides back down to the bottom. When it reaches the bottom of the incline again, it is traveling with a speed of 3.80 m/s. If the coefficient of kinetic friction between the block and the plane is 0.500, how far up the incline did the block slide?
The initial speed of a 2.58-kg box traveling up a plane inclined 37° to the horizontal...
The initial speed of a 2.58-kg box traveling up a plane inclined 37° to the horizontal is 4.55 m/s. The coefficient of kinetic friction between the box and the plane is 0.30. (a) How far along the incline does the box travel before coming to a stop? ---m (b) What is its speed when it has traveled half the distance found in Part (a)? ---m/s
A block with mass m = 14.6 kg slides down an inclined plane of slope angle...
A block with mass m = 14.6 kg slides down an inclined plane of slope angle 15.8 ° with a constant velocity. It is then projected up the same plane with an initial speed 4.35 m/s. How far up the incline will the block move before coming to rest?
1) a) A block of mass m slides down an inclined plane starting from rest. If...
1) a) A block of mass m slides down an inclined plane starting from rest. If the surface is inclined an angle theta above the horizontal, and the block reaches a speed V after covering a distance D along the incline, what is the coefficient of kinetic friction? b) at a distance D1 (still on the incline), the block comes to an instantaneous standstill against a spring with spring constant k. How far back up does the block? Why do...
4) A 5.0 kg box slides 2.00 m down a ramp that is inclined at 300...
4) A 5.0 kg box slides 2.00 m down a ramp that is inclined at 300 below the horizontal. The coefficient of kinetic friction between the box and the ramp’s surface is 0.20 a) What is the work done by gravity? b) What is the work done by the normal force? c) What is the work done by friction? d) What is the net work done on the package? e) If the box starts from rest, what is its speed...
A 47.75 kg crate slides down a 53.13* slope (inclined plane) that is 36.00 m in...
A 47.75 kg crate slides down a 53.13* slope (inclined plane) that is 36.00 m in length and has a kinetic friction coefficient of 0.444.   The create is given a downward speed of only 4.5 m/s as it starts down from the top of the slope. Applying the principle of the conservation of mechanical energy in the presence of dissipative forces, determine its final speed as it reaches the bottom of the slope.
A construction worker pushes on a 10 kg crate down an inclined plane that is 7.0...
A construction worker pushes on a 10 kg crate down an inclined plane that is 7.0 m long and is inclined at an angle of 20 degrees to the horizontal. As a result, the crate slides down the entire length of the plane with a constant speed of 3.0 m/s. Suppose that the worker pushes directly on the crate in a direction parallel to the incline with a force of 50 N for the entire length of the plane. A)...
A brick of mass 1.7 kg was pushed down a roof with an initial velocity of...
A brick of mass 1.7 kg was pushed down a roof with an initial velocity of 0.4 m/s. The roof is inclined at 21.9o with respect to the horizontal, and the coefficient of dynamic friction between the roof and the brick is 0.7. The edge of the roof is 3.9 m from where the brick was pushed. How fast will the brick be moving when it reaches the edge of the roof (in m/s)? Or, perhaps, the brick will not...