Tracy (of mass 49 kg) and Tom (of mass
65 kg) are standing at rest in the center of the
roller rink, facing each other, free to move.
Tracy pushes off Tom with her hands and remains in contact with Tom’s hands, applying
a constant force for 0.5 s. Tracy moves 0.35 m
during this time. When she stops pushing off
Tom, she moves at a constant speed.
What is Tracy’s constant acceleration during her time of contact with Tom?
Answer in units of m/s
2
12
To find Tracy's constant acceleration during her time of contact with Tom, we need to use the equation:
acceleration = (change in velocity) / (time taken)
Since Tracy starts at rest and moves at a constant speed after pushing off Tom, her change in velocity is equal to her final velocity. The final velocity can be found using the equation:
final velocity = (distance traveled) / (time taken)
Given that Tracy moves 0.35 m in 0.5 s, we can substitute these values into the equation to find the final velocity:
final velocity = 0.35 m / 0.5 s = 0.70 m/s
Since Tracy started at rest, her initial velocity is 0 m/s. Therefore, her change in velocity is equal to her final velocity.
Now we can substitute the values into the first equation to find Tracy's constant acceleration:
acceleration = (change in velocity) / (time taken) = 0.70 m/s / 0.5 s = 1.40 m/s^2
Therefore, Tracy’s constant acceleration during her time of contact with Tom is 1.40 m/s^2.
To find Tracy's constant acceleration during her time of contact with Tom, we can use Newton's second law of motion. This law states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.
We know that Tracy applies a constant force on Tom for 0.5s, causing her to move 0.35m. To find her acceleration, we need to determine the net force acting on her.
Using Newton's second law:
Net force = mass * acceleration
We can rearrange this equation to solve for acceleration:
Acceleration = Net force / mass
Now, let's calculate the net force acting on Tracy. The net force is caused by the force Tracy applies to Tom, and the reaction force Tom applies to Tracy.
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So, the force Tracy applies to Tom is equal in magnitude but opposite in direction to the force Tom applies to Tracy.
Let's assume Tracy applies a force of F on Tom. Then, Tom exerts an equal and opposite force (-F) on Tracy.
To calculate the net force, we need to consider that Tracy and Tom are at rest initially and start to move together once Tracy applies the force. The net force should overcome their inertia to start moving.
Considering the force Tracy applies, the net force can be calculated as:
Net force = Force applied by Tracy - Force applied by Tom
Net force = F - (-F) = 2F
Now, we can calculate the acceleration:
Acceleration = Net force / mass
Acceleration = 2F / (mass of Tracy)
Since the masses of Tracy and Tom are given as 49 kg and 65 kg, respectively, we can substitute the values:
Acceleration = 2F / 49 kg
We don't have the value of the force applied, but we can't determine the exact acceleration without it.
Therefore, without knowing the amount of force Tracy applied to Tom, we cannot calculate Tracy's constant acceleration during her time of contact with Tom.