Question

A 150.0 kg cart rides down a set of tracks on four solid steel wheels, each with radius 20.0 cm and mass 45.0 kg. The tracks slope downward at an angle of 17 ∘ to the horizontal. If the cart is released from rest a distance of 12.5 m from the bottom of the track (measured along the slope), how fast will it be moving when it reaches the bottom? Assume that the wheels roll without slipping, and that there is no energy loss due to friction.

Answer #1

Sol::

Given:

Cart mass (M) = 150.0 kg

Number of wheels= 4

radius(r)= 0.2 m

mass(m)= 45.0 kg.

angle Ѳ = 17°

distance(d)= 12.5 m

As per given data we have

Potential energy at top = kinetic energy of cart and wheels at
bottom + rotational energy of wheels at bottom

i .e

(M+4m)gh = 1/2 (M+4m) v² + 4(1/2 Iω²)

Where

The height (h) will be

sin 17° = h / 12.5

h = 3.654 m

And

For disks about the z-axis,we have

I = mr² / 2

So

(M+4m)gh = 0.5*(M+4m)v² + 4(0.5(mr²/2) ω²)

(M+4m)gh = 0.5 *(M+4m)v² + m r² ω²

As ω= v/r

(M+4m)gh = 0.5*(M+4m)v² + m v²

(M+4m)gh = v²(0.5M+2m+m)

v² =(M+4m)gh /(0.5M+3m)

v = √[(150+4*45)*9.8*3.65/(0.5*150+3*45)]

v = 7.497 m/s

Hope this answer helps you

Please RATE my answer

Thank you

A 150.0 kg cart rides down a set of tracks on four solid steel
wheels, each with radius 20.0 cm and mass 45.0 kg. The tracks slope
downward at an angle of 25 ∘∘ to the horizontal. If the cart is
released from rest a distance of 28.0 mm from the bottom of the
track (measured along the slope), how fast will it be moving when
it reaches the bottom? Assume that the wheels roll without slipping
and that there...

A cart of mass m = 1.2 kg is placed on a horizontal track. The
cart rolls with very little friction, and is attached to the left
end of the track by a spring with negligible mass, spring constant
k = 20.0 N/m, and un-stretched length 25.0 cm.
(A) The cart is moved 7.5 cm to the left of its equilibrium
position, and is then released from rest. Draw a sketch of the
position x along the track of the...

ch 6
1:
It is generally a good idea to gain an understanding of the
"size" of units. Consider the objects and calculate the kinetic
energy of each one.
A ladybug weighing 37.3 mg
flies by your head at 3.83 km/h
.
×10
J
A 7.15 kg
bowling ball slides (not rolls) down an alley at 17.5 km/h
.
J
A car weighing 1260 kg
moves at a speed of 49.5 km/h.
5:
The graph shows the ?-directed force
??...

Two boxes are stacked, with box B placed on top of box A. If box
A is pushed such that both boxes move with a decreasing speed, is
there any friction on either box?
(a) Kinetic friction on box A and no friction on box B (b)
Kinetic friction on box A and static friction on box B
(c) Kinetic friction on box A and kinetic friction on box B (d)
Static friction on box A and kinetic friction on...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 9 minutes ago

asked 30 minutes ago

asked 33 minutes ago

asked 39 minutes ago

asked 40 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago