Posted by sandhu on Thursday, November 25, 2010 at 6:23am.
A block starts with a speed of 18.0 m/s and slides for a distance of 2.2 m down a 40° ramp (ìk = 0.43). What is its final speed? (m/s)
physics - drwls, Thursday, November 25, 2010 at 9:19am
Final KE = PE loss - (work done against friction)
(1/2)M V^2 = M g L sin40 - M g L cos40*0.43
L = 2.2 m. Cancel out the M's and solve for V^2.
physics - sandhu, Thursday, November 25, 2010 at 9:44am
What about the initial speed of 18.0 m/s when it starts?
To calculate the final speed of the block, we need to consider the initial speed, the distance traveled, the angle of the ramp, and the coefficient of kinetic friction.
The initial speed of 18.0 m/s is not directly used to calculate the final speed. Instead, it contributes to the initial kinetic energy of the block.
The formula used to find the final speed involves the concept of conservation of energy. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
In this case, we need to consider the potential energy loss (PE loss) as the block slides down the ramp and the work done against friction.
The formula for the final kinetic energy is:
Final KE = PE loss - (work done against friction)
To calculate the potential energy loss, we need to use the formula:
PE loss = M * g * L * sin(angle)
where M is the mass of the block, g is the acceleration due to gravity, L is the distance traveled down the ramp, and angle is the angle of the ramp.
To calculate the work done against friction, we need to use the formula:
Work done against friction = M * g * L * cos(angle) * coefficient of kinetic friction
where M is the mass of the block, g is the acceleration due to gravity, L is the distance traveled down the ramp, angle is the angle of the ramp, and the coefficient of kinetic friction is given as 0.43 (ìk = 0.43).
By substituting the given values and solving the equation, we can find the final kinetic energy. Then, by taking the square root of the final kinetic energy, we can find the final speed of the block.