You are in the bleachers at the world series and a game winning baseball (mass 0.15 kg) approaches at 28 m/s. you want to catch it, but you don't want to hurt your had since that might impede your ability to do physics homework. to lessen the impact you slow it down with your hand over a displacement of 0.8 m as you catch it. what external work must you do on the baseball in j?

58.8 Joules work must be done

Explanation:

Equations of motion related distance, velocity and acceleration:

v² - v₀² = 2 x acc x Δdistance

so acc = (0 - 28²)/ (2 x 0.8 m) = -490 m/s² (negative acceleration means deceleration)

Ave force F to decelerate mass 0.15 kg = m x a = 0.15 x 490 = 73.5 Newtons

Work done W = Force x distance = 73.5 N x 0.8 m = 58.8 Nm (i.e. Joules)

here we will use the torque balance about the knee joint

here we can say that

here torque due to weight is given as

now torque due to applied force of muscle

now by torque balance we will have

so here the magnitude of m will be 173 N