Two boxes are on frictionless ramps (Speed and KE)

In summary: So in this case, the heavier box has more mass and thus has more gravitational potential energy. So it would have been faster than the lighter box.
  • #1
Koskesh
10
0

Homework Statement


Two boxes are resting on frictionless ramps. Box 1 is lighter and sits on a steep ramp while Box 2 is heavier and sits on ramp that is less steep. The boxes are released from the same point.

Which box (if either) has
a) The greater speed?
b) The greater kinetic energy at B


Homework Equations


Box 1 = Lighter and steeper ramp
Box 2 = Heaver and less steep ramp
Initial starting point = A
Displacement = B


The Attempt at a Solution


I'm sure its wrong. I don't really have a concise explanation.
a) Box 1 should have the greater speed because gravity will produce a greater effect on a higher slope.
b) Box 2 should have greater kinetic energy at B because it has more mass and thus can create higher momentum.
 
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  • #2
Hint: Consider the fact that mechanical energy is conserved on the frictionless ramps. What can you deduce from that?
 
  • #3
Doc Al said:
Hint: Consider the fact that mechanical energy is conserved on the frictionless ramps. What can you deduce from that?

Meaning there is no kinetic or potential energy present? So then neither box would be quicker than the other?
 
  • #4
Koskesh said:
Meaning there is no kinetic or potential energy present?
:confused:

What's the initial energy of each box? The final energy? How do the speeds compare?
 
  • #5
Hmm.. no initial energy? Marketing grad here boss, bear with me.. lol.
 
  • #6
Both boxes start out at some initial height (presumably the same for both boxes) so they have gravitational potential energy. What's the expression for gravitational PE as a function of height (with respect to the ground)?
 
  • #7
Work? F x D?
 
  • #8
Expression for Grav. Potential energy when the body is close to the earth?
 
  • #9
Koskesh said:
Work? F x D?
That is the work done by a constant force F over a displacement d.

Think about the expression for grav. potential energy..
 

What is speed?

Speed is a measure of how fast an object is moving. It is calculated by dividing the distance traveled by the time it took to travel that distance.

What is kinetic energy (KE)?

Kinetic energy is the energy an object possesses due to its motion. It is calculated by multiplying half of the object's mass by its velocity squared.

How does the speed of an object affect its kinetic energy?

The speed of an object directly affects its kinetic energy. As an object's speed increases, its kinetic energy also increases. This means that the faster an object is moving, the more energy it possesses.

What is a frictionless ramp?

A frictionless ramp is a surface with no friction, meaning there is no resistance or force that opposes the motion of an object. This allows objects to slide down the ramp without any external forces acting on them.

How does a frictionless ramp affect the speed and KE of objects?

A frictionless ramp allows objects to maintain a constant speed as they move down the ramp, since there is no friction to slow them down. This also means that the objects' kinetic energy will remain constant as they move down the ramp.

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