A small steel ball of mass 0.29 kg is fired at a speed 17.5 m/s and runs into some soft putty, penetrating a distance of 4 cm. What is the average force experienced by the ball from the putty?
Favg=((0.5)mv^2)/(d)
=(0.5*0.29*17.5^2)/(0.04)
don't forget to convert units to match, in this case the distance into meters
To find the average force experienced by the ball from the putty, we can use the impulse-momentum principle.
Step 1: Convert the distance penetrated from centimeters to meters:
4 cm = 0.04 m
Step 2: Calculate the initial momentum of the ball using the formula:
Momentum (p) = mass (m) × velocity (v)
p = 0.29 kg × 17.5 m/s
= 5.075 kg·m/s (rounded to three decimal places)
Step 3: Use the impulse-momentum principle to calculate the average force:
Impulse (J) = change in momentum
Average force (F) = Impulse (J) ÷ Time (t)
Since the problem does not provide the time, we can rearrange the formula to solve for the impulse:
Impulse (J) = Average force (F) × Time (t)
Step 4: Determine the impulse:
Using the formula J = p - p', where p' is the final momentum (zero because the ball comes to rest),
J = 5.075 kg·m/s - 0 kg·m/s
= 5.075 kg·m/s
Step 5: Use the impulse-momentum principle to solve for the average force:
F × t = 5.075 kg·m/s
Since we don't have the value for time, we cannot solve for the average force.
To find the average force experienced by the ball from the putty, we can use the principle of impulse. Impulse is defined as the change in momentum, and it is equal to the force applied multiplied by the time over which the force is applied. In this case, the time is not given, but we can calculate it using the given information.
First, let's find the initial momentum of the ball. The momentum (p) of an object is given by the product of its mass (m) and velocity (v). Therefore, the initial momentum (p_initial) of the ball is:
p_initial = m * v
= 0.29 kg * 17.5 m/s
Next, let's calculate the final momentum of the ball. Since the ball comes to a stop after penetrating the putty, its final velocity is zero. Thus, the final momentum (p_final) of the ball is:
p_final = m * 0
= 0 kg * 0
The change in momentum is:
Δp = p_final - p_initial
= 0 - (0.29 kg * 17.5 m/s)
Now, let's calculate the time over which the force is applied. The time (t) can be found using the formula for displacement (d) with initial velocity (v_initial = 17.5 m/s), final velocity (v_final = 0), and acceleration (a) as follows:
d = ((v_initial + v_final) / 2) * t
In this case, the displacement (d) is given as 4 cm, which needs to be converted into meters to maintain consistency. Therefore, the displacement (d) becomes 0.04 m.
0.04 m = ((17.5 m/s + 0) / 2) * t
Solving for time (t):
t = (0.04 m) / (8.75 m/s)
≈ 0.004571 s
Now that we have the time, we can calculate the average force (F_average). Rearranging the impulse formula:
F_average = Δp / t
Substituting the values:
F_average = [(0 - (0.29 kg * 17.5 m/s)) / 0.004571 s]
Calculating the result will give us the average force experienced by the ball from the putty.