1) Suzie (of mass 38 kg) is roller-blading down the sidewalk going 20 miles per hour. She notices a group of workers down the walkway who have unexpectedly blocked her path, and she makes a quick stop in 2 seconds. What is Suzie’s average acceleration? Answer in units of m/s^2.
2) What force was exerted to stop Susie? Answer in units of N.
Where did this force come from?
1. the gravity
2. the friction between the ground and the skates
3. the upward force exerted by the ground
4. the friction between the air and Suzie
5. All of these
Any help with getting this question started would be great!
To find Suzie's average acceleration, we can use the following formula:
average acceleration = (final velocity - initial velocity) / time
First, we need to convert Suzie's speed from miles per hour to meters per second. We know that 1 mile is equal to 1,609.34 meters, and 1 hour is equal to 3,600 seconds. Therefore, Suzie's speed in meters per second is:
20 miles/hour * (1,609.34 meters/1 mile) * (1 hour/3,600 seconds) = 8.94 meters/second
Her initial velocity is 8.94 meters/second and her final velocity is 0 meters/second (since she comes to a stop). The time taken to stop is given as 2 seconds.
Now we can calculate her average acceleration:
average acceleration = (0 meters/second - 8.94 meters/second) / 2 seconds = -4.47 meters/second^2
Therefore, Suzie's average acceleration is -4.47 meters/second^2.
To calculate the force exerted to stop Suzie, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
force = mass * acceleration
Given that Suzie's mass is 38 kg and her acceleration is -4.47 meters/second^2, we can calculate the force:
force = 38 kg * (-4.47 meters/second^2) = -169.86 kg*m/second^2 = -169.86 N
The force exerted to stop Suzie is approximately -169.86 N, with the negative sign indicating that it is in the opposite direction of her motion.
Now, let's determine where this force comes from:
The force comes from the friction between the ground and Suzie's skates. As Suzie applies a force in the opposite direction of her motion to stop, the ground exerts an equal and opposite force to stop her, which is the force of friction. Therefore, option 2, the friction between the ground and the skates, is the correct answer.
To find Suzie's average acceleration, we can use the formula:
acceleration = (final velocity - initial velocity) / time.
1) First, let's convert Suzie's speed from miles per hour to meters per second since the unit of acceleration is meters per second squared.
1 mile = 1609.34 meters
1 hour = 3600 seconds
So, Suzie's speed in meters per second is:
20 miles/hour * 1609.34 meters/mile / 3600 seconds/hour = approximately 8.94 m/s.
Next, we plug the given values into the formula:
acceleration = (0 m/s - 8.94 m/s) / 2 s = -4.47 m/s^2.
Therefore, Suzie's average acceleration is -4.47 m/s^2.
2) To calculate the force exerted to stop Suzie, we can use Newton's second law of motion:
force = mass * acceleration.
We were given the mass of Suzie as 38 kg, and we can use the calculated acceleration from the previous question as -4.47 m/s^2.
So, the force exerted to stop Suzie is:
force = 38 kg * -4.47 m/s^2 = -170.86 N.
The negative sign indicates that the force is in the opposite direction to Suzie's motion.
As for where this force comes from, it is primarily due to the friction between the ground and Suzie's skates. The friction force acts in the opposite direction to Suzie's motion and helps bring her to a stop. The force of gravity and the upward force exerted by the ground play a role in supporting Suzie's weight but not in stopping her motion. The friction between the air and Suzie is negligible in this scenario, so it does not contribute significantly to the force exerted to stop her.
Therefore, the correct answer is option 2: the friction between the ground and the skates.