A 5.6-kg bowling ball is accelerated from rest to a velocity of 17 m/s as the bowler covers 5.0 m of approach before releasing the ball. What force is exerted on the ball during this time?
To find the force exerted on 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.
Given:
Mass (m) = 5.6 kg
Initial velocity (u) = 0 m/s (since it is from rest)
Final velocity (v) = 17 m/s
Distance traveled (s) = 5.0 m
Acceleration (a) can be found using the equation for uniform acceleration:
v^2 = u^2 + 2as
Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
a = (17^2 - 0^2) / (2 * 5)
a = 289 / 10
a = 28.9 m/s^2
Now, we can calculate the force:
Force (F) = mass (m) * acceleration (a)
F = 5.6 kg * 28.9 m/s^2
F = 162.4 N
Therefore, the force exerted on the ball during this time is 162.4 Newtons.
To find the force exerted on the ball during this time, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, we need to determine the acceleration of the ball.
First, let's calculate the time it took for the ball to reach a velocity of 17 m/s.
We can use the equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
Since the ball starts from rest (zero velocity), the equation becomes:
17 m/s = 0 + a * t
Simplifying the equation:
17 m/s = a * t
To find the acceleration, we need the time. We can calculate the time using the equation:
s = ut + (1/2)at^2
where s is the distance covered, u is the initial velocity, a is the acceleration, and t is the time taken.
Plugging in the given values:
5.0 m = 0 * t + (1/2) * a * t^2
Simplifying the equation:
5.0 m = (1/2) * a * t^2
We can solve this equation for t:
t = √(2s / a)
Plugging in the values:
t = √(2 * 5.0 m / a)
Now, let's substitute this value of t back into the initial equation to find the acceleration:
17 m/s = a * (√(2 * 5.0 m / a))
Simplifying the equation:
17 m/s = √(10 m * a)
Squaring both sides of the equation to remove the square root:
289 m^2/s^2 = 10 m * a
Now, we can solve for the acceleration:
a = 289 m^2/s^2 / 10 m
a ≈ 28.9 m/s^2
Now that we have the acceleration, we can calculate the force using Newton's second law:
F = m * a
where F is the force, m is the mass, and a is the acceleration.
Plugging in the given values:
F = 5.6 kg * 28.9 m/s^2
F ≈ 161.84 N
Therefore, the force exerted on the ball during this time is approximately 161.84 Newtons.