Question

A 9.0-kg box of oranges slides from rest down a frictionless incline from a height of...

A 9.0-kg box of oranges slides from rest down a frictionless incline from a height of 5.0 m. A constant frictional force, introduced at point A, brings the block to rest at point B. If the coefficient of kinetic friction is 0.26, what is the distance between A and B?

Homework Answers

Answer #1

Step 1:

Using Energy conservation for frictionless incline

KEi + PEi = KEf + PEf

KEi = 0, since block slides from rest

PEi = m*g*h

KEf = 0.5*m*Vf^2

where, Vf = speed of block at bottom of the incline

PEf = 0, since h = 0 at this point

So,

0 + m*g*h = 0.5*m*Vf^2

Vf = sqrt (2*g*h)

Vf = sqrt (2*9.8*5)

Vf = 9.9 m/sec

Now during frictional surface, Using energy conservation

KEi + PEi + W = KEf + PEf

PEi = PEf = 0, since h = 0

KEf = 0, since block stops after traveling some distance 'd', So at point B, speed is zero

KEi = 0.5*m*Vi^2,

here Vi = 9.9 m/sec = Velocity at the bottom of incline at point A

W = Work-done by frictional force

W = -Ff*d = -uk*N*d = -uk*m*g*d

So,

0.5*m*Vi^2 + 0 - uk*m*g*d = 0 + 0

d = Vi^2/(2*uk*g)

Using known values

d = 9.9^2/(2*0.26*9.8)

d = 19.2 m = distance between A and B

Please Upvote.

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 30-kg crate starts from rest, slides down a frictionless incline and then along a rough...
A 30-kg crate starts from rest, slides down a frictionless incline and then along a rough horizontal surface until it comes to rest. The coefficient of kinetic friction between the horizontal surface and the crate is 0.27. If the crate’s initial height is 9 m, find the distance it travels on the horizontal surface.
Starting from rest, a 4.30-kg block slides 1.80 m down a rough 30.0° incline. The coefficient...
Starting from rest, a 4.30-kg block slides 1.80 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is ?k = 0.436. (a) Determine the work done by the force of gravity. J (b) Determine the work done by the friction force between block and incline. J (c) Determine the work done by the normal force. J (d) Qualitatively, how would the answers change if a shorter ramp at a steeper angle were...
A 10 kg box slides down a long, frictionless incline of angle 30°. It starts from...
A 10 kg box slides down a long, frictionless incline of angle 30°. It starts from rest at time t = 0 at the top of the incline at a height of 18 m above ground. (a) What is the original potential energy of the box relative to the ground? ---J (b) From Newton's laws, find the distance the box travels in 1 s and its speed at t = 1 s. ---m ---m/s (c) Find the potential energy and...
A 5.0 kg box slides down a 5.0 m high frictionless hill, starting from rest, across...
A 5.0 kg box slides down a 5.0 m high frictionless hill, starting from rest, across a 2.0 m wide horizontal surface, then hits a horizontal spring with spring constant 500 N/m. The ground under the spring is frictionless, but the 2.0 m wide horizontal surface is rough with a coefficient of kinetic friction of 0.25. a. What is the speed of the box just before reaching the rough surface? b. What is the speed of the box just before...
A 2.70-kg block starts from rest at the top of a 30.0° incline and slides a...
A 2.70-kg block starts from rest at the top of a 30.0° incline and slides a distance of 1.90 m down the incline in 1.20 s. (a) Find the magnitude of the acceleration of the block. (m/s)^2 ​(b) Find the coefficient of kinetic friction between block and plane. (c) Find the friction force acting on the block. ​Magnitude N Direction (d) Find the speed of the block after it has slid 1.90 m.    (m/s^2)
Part a. Starting from rest, a 14 kg box slides down a frictionless incline that is...
Part a. Starting from rest, a 14 kg box slides down a frictionless incline that is 7 meters tall. What is the velocity of the box at the bottom of the incline? Part b. A thin hoop of mass 14 kg and radius 1.2 m rolls down an incline that is 7 meters tall. What is the velocity of the thin hoop at the bottom of the incline? Part c. A solid disk of mass 14 kg and radius 1.2...
A block of mass 13.0 kg slides from rest down a frictionless 39.0° incline and is...
A block of mass 13.0 kg slides from rest down a frictionless 39.0° incline and is stopped by a strong spring with k = 2.70 ✕ 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed? m
Starting from rest, a 2.97 kg block slides 2.44 m down a rough 39.4 ◦ incline....
Starting from rest, a 2.97 kg block slides 2.44 m down a rough 39.4 ◦ incline. The coefficient of kinetic friction between the block and the incline is 0.471. The acceleration of gravity is 9.8 m/s 2 . 1)Find the work done by the force of gravity. Answer in units of J. 2)Find the work done by the friction force between block and incline. Answer in units of J. 3)Find the work done by the normal force. Answer in units...
1.A small block of mass 3.5 kg starting from rest slides down on an incline plane...
1.A small block of mass 3.5 kg starting from rest slides down on an incline plane of height 2.0 m, 40 degrees with respect to horizontal (Fig. 2). The coefficient of kinetic friction between the block and the incline plane is 0.25. At the end of the incline plane, the block hits the top of a hemispherical mound of ice (radius 1.0 m) , loses 75% of final kinetic energy (KE=0.5mv*v) before the collision, then slide down on the surface...
Name:__________________________________________Section____ A block of mass ? = 12.0 kg is released from rest on an incline...
Name:__________________________________________Section____ A block of mass ? = 12.0 kg is released from rest on an incline angled at θ = 30 degrees. The block slides down and incline of length ? = 1.40 m along the incline, which has a coefficient of kinetic friction between the incline and the block of ?? = 0.180. The block then slides on a horizontal frictionless surface until it encounters a spring with a spring constant of ? = 205 N/m. Refer to the...