A bowling ball weighing 40.0 N initially moves at a speed of 4.90 m/s. How long must a force of 54.0 N be applied to the ball to stop it?
The ball weighing 40N has a mass given by
F = ma
40 = 9.8m
m = 4.08kg
So, a force of 54N will produce a deceleration of 54/4.08 = -13.235 m/s^2,
v = 4.9 + at
0 = 4.9 - 13.235t
t = 4.9/13.25 = .302s
To find the time required to stop the bowling ball, 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 know the force applied (54.0 N) and the mass of the object (which we can calculate using the weight of the ball).
Step 1: Calculate the mass of the bowling ball.
The weight of the bowling ball is given as 40.0 N. Weight is equal to mass multiplied by the acceleration due to gravity (9.8 m/s^2). So, we can calculate the mass using the formula:
Weight = mass × acceleration due to gravity
40.0 N = mass × 9.8 m/s^2
mass = 40.0 N / 9.8 m/s^2
mass ≈ 4.08 kg
Step 2: Calculate the acceleration of the ball.
Since the goal is to stop the ball, we want the final velocity to be zero. The initial velocity is given as 4.90 m/s. Therefore, we can calculate the acceleration using the formula:
Final velocity^2 = Initial velocity^2 + 2 × acceleration × distance
(0 m/s)^2 = (4.90 m/s)^2 + 2 × acceleration × distance
0 = 24.01 m^2/s^2 + 2 × acceleration × distance
Since we're trying to find the time, we're not concerned with the distance. So we can consider it as being irrelevant, and simplify the equation:
0 = 24.01 m^2/s^2 + 2 × acceleration × 0
0 = 24.01 m^2/s^2
This equation tells us that the acceleration of the ball is -24.01 m^2/s^2 (note that it's negative because it's acting in the opposite direction to the initial velocity).
Step 3: Calculate the time required to stop the ball.
Now we can use Newton's second law to find the time taken to stop the ball. The net force acting on the ball is equal to the mass of the ball multiplied by its acceleration. So the equation is:
Net force = mass × acceleration
54.0 N = 4.08 kg × (-24.01 m^2/s^2)
54.0 N = -97.85 kg·m/s^2
The net force is negative because it's in the opposite direction to the initial velocity.
Now, we can find the time by rearranging the equation:
Net force = mass × acceleration
Time = Net force / (mass × acceleration)
Time = -97.85 kg·m/s^2 / (4.08 kg × -24.01 m^2/s^2)
Time ≈ 1.26 seconds
Therefore, a force of 54.0 N must be applied to the bowling ball for approximately 1.26 seconds in order to stop it.
To answer this question, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. In this case, the force being applied is to stop the bowling ball.
First, we need to find the mass of the bowling ball. We can use the equation F = m * a, where F is the force applied, m is the mass, and a is the acceleration. In this case, the force applied is 40.0 N and the acceleration is negative (since we want to stop the ball), so we'll use:
40.0 N = m * (-a).
Next, we know that acceleration is equal to the change in velocity over time. In this case, we want to find the time it takes to stop the ball, so the final velocity will be 0 m/s. Therefore, the equation becomes:
a = (0 m/s - 4.90 m/s) / t.
Now we have two equations:
40.0 N = m * (-a) --------- (1)
a = (0 m/s - 4.90 m/s) / t --------- (2)
We can substitute equation (2) into equation (1) to solve for the mass:
40.0 N = m * (4.90 m/s) / t.
Simplifying, we have:
40.0 N * t = (4.90 m/s) * m.
Rearranging the equation, we get:
m = (40.0 N * t) / (4.90 m/s).
Now we can substitute the value of m into equation (2) and solve for t:
(0 m/s - 4.90 m/s) / t = (40.0 N * t) / (4.90 m/s).
Cross multiplying, we have:
-4.90 m/s * t = 40.0 N * t.
Dividing both sides by t, we cancel out t and solve for it:
-4.90 m/s = 40.0 N.
Finally, we can divide both sides by -4.90 m/s to solve for t:
t = 40.0 N / 4.90 m/s = 8.16 seconds.
Therefore, a force of 54.0 N must be applied to the bowling ball for 8.16 seconds in order to stop it.