As a protest against the umpire’s calls, a baseball
pitcher throws a ball straight up into the
air at a speed of 20.4 m/s. In the process, he
moves his hand through a distance of 1.57 m.
The acceleration of gravity is 9.8 m/s
2
.
If the ball has a mass of 0.147 kg, find
the force he exerts on the ball to give it this
upward speed.
Answer in units of N.
force=g+ a
to find a,
Vf^2=2ad
a=(20.4)^2/(2*1.57)
To find the force exerted by the pitcher on the ball, we can use Newton's second law of motion which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the force exerted by the pitcher on the ball is the force required to accelerate the ball from rest to a speed of 20.4 m/s in the upward direction.
First, let's find the acceleration of the ball using the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (20.4 m/s)
u = initial velocity (0 m/s, as the ball starts from rest)
a = acceleration
s = distance (1.57 m)
Rearranging the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the values:
a = (20.4^2 - 0) / (2 * 1.57)
a = 663.36 / 3.14
a ≈ 211.23 m/s^2 (rounded to two decimal places)
Now, we can use Newton's second law to find the force (F):
F = m * a
Where:
m = mass of the ball (0.147 kg)
a = acceleration (211.23 m/s^2)
Substituting the values:
F = 0.147 * 211.23
F ≈ 31.06 N (rounded to two decimal places)
Therefore, the force exerted by the pitcher on the ball to give it an upward speed of 20.4 m/s is approximately 31.06 N.
To find the force exerted by the pitcher on the ball, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
In this case, the acceleration is due to the force of gravity, so we can use the gravitational acceleration (g) of 9.8 m/s^2.
We can start by calculating the acceleration due to the upward motion of the ball. Since the ball is thrown straight up, its acceleration will be in the opposite direction of gravity and will be negative. We can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance.
Given:
Initial velocity (u) = 20.4 m/s (upward)
Distance (s) = 1.57 m
Using the equation, we can solve for the downward acceleration (a):
0 = (20.4 m/s)^2 - 2a(1.57 m)
Rearranging the equation:
a = - ((20.4 m/s)^2 / (2 * 1.57 m))
Calculating the value of a:
a ≈ - 131.22 m/s^2
Now, we can calculate the force (F) exerted by the pitcher on the ball:
F = m * a
Given:
Mass (m) = 0.147 kg
Acceleration (a) = - 131.22 m/s^2 (downward)
Calculating the force:
F = (0.147 kg) * (-131.22 m/s^2)
F ≈ -19.32 N
Since we're looking for the magnitude of the force, we can take the absolute value of the negative force:
F ≈ 19.32 N
Therefore, the force exerted by the pitcher on the ball to give it an upward speed of 20.4 m/s is approximately 19.32 N.