a metal ball falls from a. height 1m onto a. steel. plate and jump. up. to a. height of. 0.81m. .find. the. coefficient of restitution
since v = √(2as)
v for a 1m fall is √19.2
v for a .81m bounce is √(.81*19.2) = .9√19.2
so, the c.r is 0.9
it's just the √ of the bounce-height ratio.
To find the coefficient of restitution, we need to use the equation:
e = √(h2/h1),
where:
e is the coefficient of restitution,
h1 is the initial height of the ball,
h2 is the height the ball rebounds to.
In this case, the ball falls from a height of 1m (h1 = 1m) and rebounds to a height of 0.81m (h2 = 0.81m). So, we can plug these values into the equation:
e = √(0.81/1)
e = √(0.81)
Now, to evaluate this expression, we need to find the square root of 0.81. Taking the square root of a number is equivalent to raising it to the power of 1/2. So we have:
e = (0.81)^(1/2)
e ≈ 0.9
Therefore, the coefficient of restitution is approximately 0.9.
The coefficient of restitution (e) is a measure of the elasticity of a collision between two objects. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach between the two objects.
In this case, we can find the coefficient of restitution by using the equation:
e = √(h_r / h_f)
where h_r is the rebound height and h_f is the initial drop height.
Given:
Initial drop height, h_f = 1 m
Rebound height, h_r = 0.81 m
Applying the equation:
e = √(0.81 / 1)
e = √0.81
e ≈ 0.9
Therefore, the coefficient of restitution for the ball and steel plate collision is approximately 0.9.