During a play, a tennis player hits the ball when its velocity is 20 m/s towards him. The racquet exerts a force of 540N on the ball for 6.90 ms, giving its returning velocity of 42 m/s.
Find the mass of the ball
F•Δt=Δp=mΔv=m[v₂-(-v₁)]=m(v₂+v₁)
m= F•Δt/ (v₂+v₁)=540•6.9•10⁻³/(42+20) = 0.06 kg
thanks!!
To solve this problem, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, we need to calculate the acceleration of the ball using the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Substituting the given values into the equation, we get:
Acceleration = (42 m/s - 20 m/s) / (6.90 ms)
Next, we need to convert the time from milliseconds to seconds by dividing it by 1000:
Acceleration = (42 m/s - 20 m/s) / (6.90 ms / 1000)
Simplifying this expression:
Acceleration = (42 m/s - 20 m/s) / (0.00690 s)
Now that we have the acceleration, we can calculate the mass of the ball by rearranging Newton's second law:
Mass = Force / Acceleration
Substituting the given force and calculated acceleration into the equation:
Mass = 540 N / Acceleration
Finally, we can substitute the calculated acceleration into the expression to find the mass of the ball.