To celebrate a victory, a pitcher throws her glove straight upward with an initial speed of 6.12 m/s. The throwing action requires a distance of 30.3 cm. If the glove has a mass 143 grams, what is the force acting on the glove?
v^2 = 2as
F = ma
watch the units
To find the force acting on the glove, we need to use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
First, we need to convert the initial velocity from cm/s to m/s.
Given: Initial velocity (v) = 6.12 m/s
Distance (d) = 30.3 cm
1 m = 100 cm
Therefore, the initial velocity (v) in m/s is:
v = 6.12 m/s
Next, we need to find the acceleration. To do that, we can use the kinematic equation:
v^2 = u^2 + 2ad
Where:
v = final velocity (0 m/s when the glove reaches its maximum height)
u = initial velocity
a = acceleration
d = distance
Rearranging the equation, we have:
a = (v^2 - u^2) / (2d)
Substituting the values:
a = (0^2 - (6.12)^2) / (2 * 0.303 m)
After calculating, we find that the acceleration (a) is approximately -60.742 m/s². The negative sign indicates that the acceleration is in the opposite direction of the initial velocity because the glove is moving upward and slowing down.
Next, we can calculate the force using Newton's second law:
Force (F) = mass (m) * acceleration (a)
Given:
Mass (m) = 143 grams = 0.143 kg
Acceleration (a) = -60.742 m/s²
After substituting the values and calculating, we find that the force acting on the glove is approximately -8.721 N. The negative sign indicates that the force is downward, opposite to the direction of the glove's initial velocity.