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mestny [16]
3 years ago
15

A 0.023 kg golf ball moving at 18.9 m/s crashes through the window of a house in 5.4 × 10−4 s. After the crash, the ball contin-

ues in the same direction with a speed of 10.1 m/s.
Assuming the force exerted on the ball by the window was constant, what was the mag- nitude of this force?
Answer in units of N.
Physics
1 answer:
PolarNik [594]3 years ago
7 0
Force can be expressed as the time-rate change of momentum

Mathematically, Force = Change in momentum/change in time

Change in momentum = m(10.1-18.9) = -0.2024

Force = -2024/5.4 = -375N(approx)

The significance of the '-' sign is that the direction of force is the opposite that of the direction of our velocities since we assumed them to be positive.

Also this is the force on the ball, the force on the window will be equal and opposite.
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1) 29.4 N

The force of gravity between two objects is given by:

F=G\frac{Mm}{r^2}

where

G is the gravitational constant

M and m are the masses of the two objects

r is the separation between the centres of mass of the two objects

In this problem, we have

M=5.97\cdot 10^{24} kg (mass of the Earth)

m=3.0 kg (mass of the box)

r=R=6.37\cdot 10^6 m (Earth's radius, which is also the distance between the centres of mass of the two objects, since the box is located at Earth's surface)

Substituting into the equation, we find F:

F=\frac{(6.67\cdot 10^{-11})(5.97\cdot 10^{24})(3.0)}{(6.37\cdot 10^6)^2}=29.4 N

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Let's now calculate the ratio F/m. We have:

F = 29.4 N

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Subsituting, we find

\frac{F}{m}=\frac{29.4}{3.0}=9.8 N/kg = 9.8 m/s^2

This is called acceleration of gravity, and it is the acceleration at which every object falls near the Earth's surface. It is indicated with the symbol g.

We can prove that this is the acceleration of the object: in fact, according to Newton's second law,

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