A 0.023 kg golf ball moving at 15.7 m/s crashes through the window of a house in 5.3 × 10−4 s. After the crash, the ball continues in the same direction with a speed of 11.4 m/s. Assuming the force exerted on the ball by the window was constant, what was the magnitude of this force? Answer in units of N.

Magnitude of the force exerted on the window = 186.6 N

Explanation:

Impulse = change in momentum

Impulse = force × time period during which it acts = F × t = Ft

Change in momentum = m(v₁ - v₂)

m = 0.023 kg, v₁ = 15.7 m/s, v₂ = 11.4 m/s

Change in momentum = 0.023 (15.7 - 11.4) = 0.0989 kgm/s

Impulse = change in momentum = 0.0989

Ft = 0.0989

t = 5.3 × 10⁻⁴ s = 0.00053

F = 0.0989/0.00053 = 186.6 N

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.