Kinetic motions and diagrams

Question

1. The diagram below represents a track which has been erected to demonstrate certain aspects of the energy of a body. A small cart of mass 4.0kg moves without friction on the track, with a speed of 10m/s^-1 along AB.

http://www.flickr.com/photos/99973477@N03/9560399344/

a) what is the kinetic energy of the cart as it moves along AB?

b) at which point on the track is its kinetic energy a maximum?

c) what is the change in the potential energy of the cart between B and D?

d) what is the kinetic energy of the cart as it moves along the horizontal level DE?

e) calculate the speed of the cart as it passes the point C

2. A mass of 2.0kg initially travelling at 10m/s^-1 moves up the line of greatest slope of a frictionless inlcline which makes an angle of 30degrees with the horizontal. [Take g=10m/s^-1] Find:

a) the force opposing the motion

b) the intiial kinetic energy of the mass

c) the maximum distance travelled up the incline

d) the maximum vertical height attained by the mass

Answer 1

 

a)

 

Observe the figure; the force opposing the motion is of the weight which is parallel to slope.

F = m * g * sin θ = 2 * 10 * sin 30 = 10 N

b)

Tthe initial kinetic energy of the mass can be found using formula
KE = ½ * m * v^2 = ½ * 2 * 10^2 = 100 J

d)

The obects stops when its kinetic energy decreases to 0 J as its potential energy increases to 100 J.
PE = KE

m * g * h = 100
2 * 10 * h = 100

h = 5 meters

c)

Now determine the length of the slope.

sin θ = opp/hyp = height/Length

Length = height/sin θ

L = 5 / sin 30
L = 5 / 0.5 = 10 meters
The maximum distance travelled up the incline is 10 meters.