To test a slide at an amusement park, a block of wood with mass 3.00 kgkg is released at the top of the slide and slides down to the horizontal section at the end, a vertical distance of 23.0 mm below the starting point. The block flies off the ramp in a horizontal direction and then lands on the ground after traveling through the air 30.0 mm horizontally and 40.0 mm downward. Neglect air resistance.

How much work does friction do on the block as it slides down the ramp?

This question involves the concepts of the law of conservation of energy and the equations of motion.

The work done by the friction on the block as it slides down the ramp is "0.51 J".

First, we will find the time taken for the motion using the second equation of motion in the vertical direction:

where,

h = vertical distance covered by the block = 40 mm = 0.04 m

vi = initial speed in vertical direction = 0 m/s

t = time taken = ?

g = acceleration due to gravity = 9.81 m/s^2

Therefore,

Now, we will consider the horizontal motion. Since horizontal motion is uniform due to no friction. Therefore,

where,

s = horizontal distance covered by the block = 30 mm = 0.03 m

v = final horizontal speed = ?

Therefore,

v = 0.333 m/s

Now, we apply the law of conservation of energy to this scenario:

here,

W = work done by friction = ?

h = height of slide = 23 mm = 0.023 m

m = mass of block = 3 kg

Therefore,

W = 0.677 J - 0.167 J

W = 0.51 J = 510 mJ

Learn more about the law of conservation of energy here:

link

The attached picture explains the law of conservation of energy.

511.1 J

Explanation:

We are given that

Mass of wood block=m=3 kg

Vertical distance,h=23 m

Horizontal distance =x=30 m

Distance traveled in downward direction y=40 m

Initial velocity,u=0

Where

By work energy theorem

Change in kinetic energy=Work done= mgh-W

Hence, the work done due to friction on the block as it slides down the ramp=511.1 J