Under the action of a constant net force, a 3.1-kg object moves a distance of 15 meters in 8.99 seconds starting from rest. What is the magnitude of this net force?
I got the answer of 0.58 Newtons, but the book says the solution is 1.2 Newtons.
To get this I found the velocity by displacement divided by time (15m/8.99s) = 1.7 m/s. Then got the acceleration by dividing velocity by time (1.7m/s / 8.99s) = 0.19m/s/s
I then plugged this acceleration into F=m*a, using the mass given in the problem to find the force. According to the book's solution however, the acceleration should be .38m/s/s, correct?
The acceleration a is
a = 2 X/t^2 = 0.371 m/s^2
The force is M a = 1.151 N
They apparently want you to round off to two significant figures, hence the 1.2.
Your mistake arises from mixing up final velocity with average velocity.
To calculate the magnitude of the net force acting on an object, you can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a).
In this case, you correctly calculated the displacement and time, which can be used to find the average velocity. However, you made a mistake by assuming this average velocity is equal to the final velocity of the object.
To find the average velocity, divide the displacement (15m) by the time (8.99s) as you did, which gives you 1.67 m/s. However, you need to find the acceleration by dividing the change in velocity by the time taken.
To find the change in velocity, subtract the initial velocity (which is zero since the object starts from rest) from the final velocity. In this case, the final velocity is the average velocity (1.67 m/s) because the acceleration is constant. Therefore, the change in velocity is also 1.67 m/s.
Now divide the change in velocity by the time to get the acceleration: 1.67 m/s divided by 8.99 s = 0.19 m/s². This is the correct value for acceleration.
Next, multiply the mass (3.1 kg) by the acceleration (0.19 m/s²) to find the net force: 3.1 kg × 0.19 m/s² = 0.589 N.
Rounding this value to two significant figures gives you 0.59 N, not 0.58 N as you mentioned. It seems the book solution rounded off incorrectly; therefore, your answer of 0.58 N is closer to the correct value.
Remember, when performing calculations, it is essential to use the correct formulas and ensure you are correctly interpreting the given values in the problem.