Question

A small block of mass 53 g is released from
rest at the top of a curved frictionless wedge
of mass 370 g which sits on a frictionless
horizontal surface as shown.
The acceleration due to gravity is
9.81 m/s
2
. Right is the positive direction.
When the block leaves the wedge, its velocity is 3.64 m/s to the right.
What is the height h of the wedge in meters?

Answer 1

This is a tricky one. I'm assuming that both the wedge and block move?

Answer 2

yes

Answer 3

the wedge moved at a velocity of -.521m/s

Answer 4

that is the first part of it

Answer 5

but it asks for the height

Answer 6

We can use conservation of energy here.

The initial energy of the system must equal the final energy of the system.

Initially, the wedge is not moving and is resting on the ground. Therefore, it has no energy. The block is not moving but is at the top of the wedge. Therefore, it has potential energy.

The potential energy of the block must equal the total kinetic energy of the wedge and block once the block reaches the ground. \[m_b g h = {1 \over 2} m_b v_b^2 + {1 \over 2} m_wv_w^2\]

Answer 7

basically it is 9.81h=.5(3.64^2+-(.521^2))?

Answer 8

sry it would be .423(9.81)h= .5(.053)(3.64^2)+.5(.370)(-(.521^2)?

Answer 9

The energy of the wedge will be positive (the negative velocity is squared, making it positive).

Answer 10

hmmmm why? I would be opposite direction right?

Answer 11

it

Answer 12

I have only the last try -.- sad

Answer 13

Yes but energy is a scaler quantity. It does not have direct.

Answer 14

so .423(9.81)h= .5(.053)(3.64^2)+.5(.370)(.521^2) is the equation?

Answer 15

or .370(9.81)h?

Answer 16

Neither. The 53gram mass is the one elevated.

Answer 17

will it be just
9.81h=.5(.521^2)?

Answer 18

No. Both masses move. The potential energy of the 53g block is converted into the kinetic energy of the 53g block AND of the 370g wedge. The wedge possesses no potential energy initially.

Answer 19

Will it be .772m?

Answer 20

I worried if I type this time wrong I will miss the point

Answer 21

Yes. That is correct.

Answer 22

hu......thx and the final one is coming -.- I just stress on the explainings