A major-league catcher gloves a 92 {\rm mi}/{\rm h} pitch and brings it to rest in 0.15 {\rm m}.
1-If the force exerted by the catcher is 803 {\rm N}, what is the mass of the ball?
correction
i- 92 mi/h
ii- 0/15 m
iii- 803 N
To find the mass of the ball, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the force exerted by the catcher is given as 803 N, and we need to find the mass of the ball.
The acceleration of the ball can be calculated using the kinematic equation:
v^2 = u^2 + 2as
where v is the final velocity (which is zero because the ball comes to rest), u is the initial velocity (92 mph), a is the acceleration, and s is the displacement (0.15 m).
First, we need to convert the initial velocity from miles per hour (mph) to meters per second (m/s).
1 mile = 1.60934 km
1 km = 1000 m
1 hour = 3600 s
So, to convert mph to m/s, we can use the following conversion factors:
92 mph * (1.60934 km/1 mile) * (1000 m/1 km) * (1 hour/3600 s) = 41.15 m/s (rounded to two decimal places)
Now we can use the kinematic equation to find the acceleration:
0 = (41.15 m/s)^2 + 2 * a * 0.15 m
Simplifying the equation, we have:
0 = 1691.72 m^2/s^2 + 0.3 a
Dividing both sides by 0.3:
-1691.72 m^2/s^2 = a
Now we can substitute the acceleration into Newton's second law:
803 N = m * (-1691.72 m^2/s^2)
Rearranging the equation to solve for the mass:
m = 803 N / (-1691.72 m^2/s^2)
Calculating this, we find:
m ≈ -0.475 kg
The negative sign indicates that there might be an error in our calculation. The most common reason for this type of discrepancy is rounding errors. Make sure to use sufficient decimal places throughout the calculation to minimize rounding errors.