A ball of mass m moves with speed `v` and it strikes normally with a wall and reflected back normally, if its time of contact with wall is `t` then find force exerted by ball on wall

Options

A. `(2mv)/(t)`
B. `(mv)/(t)`
C. mvt
D. `(mv)/(2t)`

Answer

To find the force exerted by the ball on the wall when it strikes and reflects back, we can follow these steps:

### Step 1: Understand the Initial and Final Momentum
When the ball strikes the wall, it has an initial momentum given by:
\[ p_{\text{initial}} = mv \]
where \( m \) is the mass of the ball and \( v \) is its velocity.

After striking the wall and reflecting back, the ball's velocity becomes \( -v \) (the negative sign indicates the direction is opposite). Thus, the final momentum is:
\[ p_{\text{final}} = m(-v) = -mv \]

### Step 2: Calculate the Change in Momentum
The change in momentum (\( \Delta p \)) can be calculated as:
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} \]
Substituting the values we found:
\[ \Delta p = (-mv) - (mv) = -mv - mv = -2mv \]

### Step 3: Relate Change in Momentum to Force
The force exerted by the ball on the wall can be calculated using the formula:
\[ F = \frac{\Delta p}{\Delta t} \]
where \( \Delta t \) is the time of contact with the wall, which is given as \( t \).

Substituting the change in momentum:
\[ F = \frac{-2mv}{t} \]

### Step 4: Determine the Magnitude of the Force
Since force is typically expressed as a positive value when discussing magnitude, we can write:
\[ F = \frac{2mv}{t} \]

### Final Answer
The force exerted by the ball on the wall is:
\[ F = \frac{2mv}{t} \]

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