When spiking a volleyball, a player changes the velocity of the ball from 4.5 m/s to -20 m/s along a certain direction.
If the impulse delivered to the ball by the player is -9.7 kg * m/s,
what is the mass of the volleyball?
momentum is P=MV
P is impulse, which in this case is -9.7kg*m/s
V is the change is velocity so (-24.7-5.2)
so you just plug all this in the formula
-9.7=(-24.7-5.2)m
then just solve for "m" !
To find the mass of the volleyball, we can use the formula for impulse:
Impulse = Change in momentum
The formula for momentum is:
Momentum = mass * velocity
Given that the initial velocity (u) is 4.5 m/s, the final velocity (v) is -20 m/s, and the impulse (I) is -9.7 kg*m/s, we can set up the equation:
I = mv - mu
Plugging in the values we know:
-9.7 kg*m/s = m*(-20 m/s) - m*(4.5 m/s)
Simplifying:
-9.7 kg*m/s = -20m^2/s - 4.5m^2/s
Combining like terms:
-9.7 kg*m/s = -24.5m^2/s
Now, let's isolate the mass:
-9.7 kg*m/s + 24.5m^2/s = 0
Using the quadratic formula to solve for m:
m = (-b +- sqrt(b^2 - 4ac)) / 2a
In this case:
a = 24.5
b = -9.7
c = 0
Plugging in the values and solving for m:
m = (-(-9.7) +- sqrt((-9.7)^2 - 4*24.5*0)) / 2*24.5
m = (9.7 +- sqrt(94.09)) / 49
m = (9.7 +- 9.699) / 49
m = 0.395 / 49 or 19.399 / 49
m ≈ 0.008 kg or 0.396 kg
Therefore, the mass of the volleyball is approximately 0.008 kg or 0.396 kg.
To find the mass of the volleyball, we can use the principle of impulse-momentum.
The impulse delivered to an object is equal to the change in momentum of the object. Mathematically, impulse (J) is given by the product of force (F) and the time (Δt) over which the force acts:
J = F * Δt
In this case, we are given that the impulse delivered to the ball is -9.7 kg * m/s. The negative sign indicates that the impulse acts in the opposite direction to the initial velocity.
The change in momentum (Δp) can be calculated as:
Δp = m * Δv
Where:
m = mass of the ball (unknown)
Δv = change in velocity = final velocity - initial velocity
We are given that the initial velocity (v1) is 4.5 m/s and the final velocity (v2) is -20 m/s. Substituting these values into the equation, we get:
Δv = v2 - v1
= -20 m/s - 4.5 m/s
= -24.5 m/s
Now, we can equate the impulse and the change in momentum:
J = Δp
-9.7 kg * m/s = m * (-24.5 m/s)
To find the mass (m), we can rearrange the equation:
m = -9.7 kg * m/s / (-24.5 m/s)
Calculating the above expression, we find:
m ≈ 0.396 kg
Therefore, the mass of the volleyball is approximately 0.396 kg.