Answer:
a. [tex]v = \frac{mu_sm_2g\Delta t}{m_1}[/tex]
b. 21.64 m/s
Explanation:
Let g = 9.81m/s2
a. The weight of the block is product of its mass and gravitational acceleration
[tex]W = m_2g = 7.25*9.81 = 71.1225N[/tex]
which is also the normal force acting on the block from the floor so it stays balanced.
N = 71.225N
The static friction of the block is product of its normal force from the floor and the friction coefficient
[tex]F_s = \mu_sN = \mu_sW = mu_sm_2g[/tex]
For the block to move, the force generated by the impact must be at least equal to the static friction.
[tex]F = F_s = mu_sm_2g[/tex]
The impulse is product of this force and time duration of impact.
[tex]I = F\Delta t = mu_sm_2g\Delta t[/tex]
As impulse is generated by change in momentum of the ball, which is product of its mass and velocity v
[tex]I = \Delta p = m_1\Delta v[/tex]
[tex]mu_sm_2g\Delta t = m_1 v[/tex]
[tex]v = \frac{mu_sm_2g\Delta t}{m_1}[/tex]
b. [tex]v = \frac{mu_sm_2g\Delta t}{m_1} = \frac{0.74*7.25*9.81*0.185}{0.45} = 21.64 m/s[/tex]
From Newton's second law, the minimum velocity the ball must have, to make the block move is 21 m/s
There are two types of collision
In elastic collision, both momentum and energy are conserved.
Given that a baseball of mass m1 = 0.45 kg is thrown at a concrete block m2 = 7.25 kg. The block has a coefficient of static friction of μs = 0.74 between it and the floor. The ball is in contact with the block for t = 0.185 s while it collides elastically.
For the concreate block to move, the force applied must be greater than the friction between the block and the floor.
The frictional force = μN
where N = mg
Friction = 7.25 x 9.8 x 0.72
Friction = 51.156
Let assume that the force applied will be equal to the friction. From Newton's second law,
F = Change in momentum / time taken.
That is
F = [tex]m_{1}[/tex]V / t
since the ball is starting from rest, the initial velocity u = 0
a. The expression for the minimum velocity the ball must have, to make the block move will be
F = [tex]m_{1}[/tex]V / t
Make V the subject of formula
V = Ft / [tex]m_{1}[/tex]
substitute F into the formula
V = μ[tex]m_{2}[/tex]g t / [tex]m_{1}[/tex]
b. The velocity in m/s will be calculated by substituting all the parameters into the formula above.
V = (51.156 x 0.185) / 0.45
V = 9.46386 / 0.45
V = 21 m/s
Therefore, the minimum velocity the ball must have, to make the block move is 21 m/s
Learn more about collision here: https://brainly.com/question/25121535
