This has been bugging me, I am given the steps to the answer, yet when I try to redo it I cannot reach the same answer. It is probably some silly mistake that I don't seem to notice, can someone please point my error, Thank you!
Context : Physics
The coefficient of friction between the block of mass m1 = 3.00 kg
and the surface in the figure below is μk = 0.395. The system starts
from rest. What is the speed of the ball of mass m2 = 5.00 kg when
it has fallen a distance h = 1.70 m?
a=g(m2-μkm1)/(m1+m2)
a= [(9.8) (5.00kg) - 0.395(3.00kg)] / (5.00kg) + (3.00kg)
a= 4.68 m/s^2
Yet when I try to do it myself, it give me a whole different number
a = g ( m2 - μk m1 ) / ( m1 + m2 ) =
9.81 ∙ ( 5 - 0.395 ∙ 3 ) / ( 5 + 3 ) =
9.81 ∙ ( 5 - 1.185 ) / 8 =
9.81 ∙ 3.815 / 8 =
37.42515 / 8 =
4.67814375
a = 4.68 m / s²
rounded on two decimal pieces
To help you identify your error, let's go through the calculation step by step.
Given:
m1 = 3.00 kg (mass of the block)
μk = 0.395 (coefficient of friction)
m2 = 5.00 kg (mass of the ball)
h = 1.70 m (distance fallen)
The formula you provided is:
a = g(m2 - μk*m1) / (m1 + m2)
Plugging in the values:
a = (9.8 m/s^2) * (5.00 kg - 0.395 * 3.00 kg) / (3.00 kg + 5.00 kg)
Now let's calculate the numerator:
numerator = (5.00 kg - 0.395 * 3.00 kg)
= (5.00 kg - 1.185 kg)
= 3.815 kg
And the denominator:
denominator = (3.00 kg + 5.00 kg)
= 8.00 kg
Now, let's calculate the acceleration:
a = (9.8 m/s^2) * (3.815 kg) / (8.00 kg)
≈ 4.64 m/s^2 (approximated to two decimal places)
So, the correct value for acceleration is approximately 4.64 m/s^2.
If you are getting a different number, maybe you made an error in your calculations. Double-check the multiplication and addition steps to ensure accuracy.